Finite Group Databasebeta

← Group #10693833

Character table — Group #10693833

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444121212121212121212121212121212121616161616161616161616162424242424242424
order122222223444444446666666888888884488881212121212121212121212122424242424242424242424242424242444444444888888884444121212121212121288888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-1
χ91-1-1111-1-111-1-1-111-11-1-1-1111-11111-1-1-1-11-111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−ii−ii−iii−i−iii−i−i11-1-111-1-1
χ101-1-1111-1-111-1-1-111-11-1-1-1111-11111-1-1-1-11-111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i−ii−ii−i−iii−i−iii-1-111-1-111
χ111-1-1111-1-111-1-1-111-11-1-1-1111-11111-1-1-1-11-111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiiii−ii−iii−i−iii−i−i-1-111-1-111
χ121-1-1111-1-111-1-1-111-11-1-1-1111-11111-1-1-1-11-111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−ii−ii−i−iii−i−iii11-1-111-1-1
χ131-1-1111-1-111-1-1-111-11-1-1-1111-1-1-1-1-111111-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−i−i−iiiiii−i−iiii−i−i−i−iii11-1-1-1-111
χ141-1-1111-1-111-1-1-111-11-1-1-1111-1-1-1-1-111111-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−i−i−iiiii−iii−i−i−iiiii−i−i-1-11111-1-1
χ151-1-1111-1-111-1-1-111-11-1-1-1111-1-1-1-1-111111-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−iii−i−iiiiiii−i−i−i−ii−i−iiii−i−i−i−iii-1-11111-1-1
χ161-1-1111-1-111-1-1-111-11-1-1-1111-1-1-1-1-111111-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−iii−i−iiiiiii−i−i−i−i−iii−i−i−iiiii−i−i11-1-1-1-111
χ17222222222222-2-2-2-22222222200000000-2-2000022-2-222-2-2-2-2-2-200000000000000002222-2-2-2-20000000000000000000000000000
χ18222222222222-2-2-2-22222222200000000-2-2000022-2-222-2-2-2-2-2-20000000000000000-2-2-2-222220000000000000000000000000000
χ19222222222-2-2-22222-2222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ20222222222-2-2-22222-22222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-222-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-2222222200000000220000-2-222-2-2-2-222-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ22222222222-2-2-2-2-2-2-2-2222222200000000220000-2-222-2-2-2-222-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2322222222-122222222-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-100000000
χ2422222222-122222222-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-21111111100000000
χ2522222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-1111100000000
χ2622222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-100000000
χ2722222222-1-2-2-22222-2-1-1-1-1-1-1-122222222-2-2-2-2-2-2111111-1-111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ2822222222-1-2-2-22222-2-1-1-1-1-1-1-122222222-2-2-2-2-2-2111111-1-111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ2922222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-22222111111-1-111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ3022222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-22222111111-1-111-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ312222-2-2-2-2200022-2-2022-22-2-2-222-2-222-2-20000000000002-2002-222-2-2000022-2-2000000000000000000000000000000002−22−22−22−2
χ322222-2-2-2-2200022-2-2022-22-2-2-222-2-222-2-20000000000002-2002-222-2-2000022-2-200000000000000000000000000000000−22−22−22−22
χ332222-2-2-2-2200022-2-2022-22-2-2-2-2-222-2-2220000000000002-2002-2-2-2220000-2-222000000000000000000000000000000002−22−2−22−22
χ342222-2-2-2-2200022-2-2022-22-2-2-2-2-222-2-2220000000000002-2002-2-2-2220000-2-22200000000000000000000000000000000−22−222−22−2
χ3522-2-22-22-2222-20000-22-22-22-2-22−22−22−22−2002−22−22-2002-20000002−22−222−2−22−22−222−2−22-22-200002−22−22−22−200000000000000000000
χ3622-2-22-22-2222-20000-22-22-22-2-22−22−22−22−2002−22−22-2002-20000002−22−222−2−22−22−222−2−2-22-220000−22−22−22−2200000000000000000000
χ3722-2-22-22-2222-20000-22-22-22-2-2−22−22−22−2200−22−222-2002-2000000−22−22−2−222−22−22−2−2222-22-20000−22−22−22−2200000000000000000000
χ3822-2-22-22-2222-20000-22-22-22-2-2−22−22−22−2200−22−222-2002-2000000−22−22−2−222−22−22−2−222-22-2200002−22−22−22−200000000000000000000
χ3922-2-22-22-22-2-22000022-22-22-2-22−22−22−22−200−22−22-2200-220000002−22−2−2−2222−22−2−2−22200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i200000000000000000000
χ4022-2-22-22-22-2-22000022-22-22-2-22−22−22−22−200−22−22-2200-220000002−22−2−2−2222−22−2−2−2220000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i200000000000000000000
χ4122-2-22-22-22-2-22000022-22-22-2-2−22−22−22−22002−22−2-2200-22000000−22−2222−2−2−22−2222−2−200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i200000000000000000000
χ4222-2-22-22-22-2-22000022-22-22-2-2−22−22−22−22002−22−2-2200-22000000−22−2222−2−2−22−2222−2−20000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i200000000000000000000
χ432-22-22-2-2222-220000-2-22-2-22-222−22−2−22−22002−2−222-200-220000002−22−222−2−2−22−22−2−2222i−2i−2i2i0000i2−i2i2−i2−i2i2−i2i200000000000000000000
χ442-22-22-2-2222-220000-2-22-2-22-222−22−2−22−22002−2−222-200-220000002−22−222−2−2−22−22−2−222−2i2i2i−2i0000−i2i2−i2i2i2−i2i2−i200000000000000000000
χ452-22-22-2-2222-220000-2-22-2-22-22−22−222−22−200−222−22-200-22000000−22−22−2−2222−22−222−2−22i−2i−2i2i0000−i2i2−i2i2i2−i2i2−i200000000000000000000
χ462-22-22-2-2222-220000-2-22-2-22-22−22−222−22−200−222−22-200-22000000−22−22−2−2222−22−222−2−2−2i2i2i−2i0000i2−i2i2−i2−i2i2−i2i200000000000000000000
χ472-22-22-2-222-22-200002-22-2-22-222−22−2−22−2200−222−2-22002-20000002−22−2−2−222−22−2222−2−200002-2-22−222−22−2−2200000000000000000000
χ482-22-22-2-222-22-200002-22-2-22-222−22−2−22−2200−222−2-22002-20000002−22−2−2−222−22−2222−2−20000-222-22−2−22−222−200000000000000000000
χ492-22-22-2-222-22-200002-22-2-22-22−22−222−22−2002−2−22-22002-2000000−22−2222−2−22−22−2−2−22200002-2-222−2−22−222−200000000000000000000
χ502-22-22-2-222-22-200002-22-2-22-22−22−222−22−2002−2−22-22002-2000000−22−2222−2−22−22−2−2−2220000-222-2−222−22−2−2200000000000000000000
χ512-2-2222-2-222-2-22-2-222-2-2-2222-200000000-22000022-2-2-2-22222-2-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ522-2-2222-2-222-2-22-2-222-2-2-2222-200000000-22000022-2-2-2-22222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ532-2-2222-2-22-2222-2-22-2-2-2-2222-2000000002-20000-2-2222222-2-2-2-200000000000000000000000022-2-2-2-22200000000000000000000
χ542-2-2222-2-22-2222-2-22-2-2-2-2222-2000000002-20000-2-2222222-2-2-2-2000000000000000000000000-2-22222-2-200000000000000000000
χ552-2-2222-2-22-222-222-2-2-2-2-2222-22222-2-2-2-2-22-2-222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ562-2-2222-2-22-222-222-2-2-2-2-2222-2-2-2-2-22222-2222-2-2-2-2-2-222-2-22222-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000
χ572-2-2222-2-2-12-2-2-222-22111-1-1-112222-2-2-2-22-222-2-2-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111100000000000000002i−2i2i−2i−i−iii−i−iii00000000
χ582-2-2222-2-2-12-2-2-222-22111-1-1-112222-2-2-2-22-222-2-2-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111110000000000000000−2i2i−2i2iii−i−iii−i−i00000000
χ592-2-2222-2-2-12-2-2-222-22111-1-1-11-2-2-2-222222-2-2-222-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i00000000
χ602-2-2222-2-2-12-2-2-222-22111-1-1-11-2-2-2-222222-2-2-222-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii00000000
χ612-2-2222-2-2-1-222-222-2-2111-1-1-112222-2-2-2-2-22-2-2221111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1000000000000000000003−3−333−3−3300000000
χ622-2-2222-2-2-1-222-222-2-2111-1-1-112222-2-2-2-2-22-2-2221111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000−333−3−333−300000000
χ632-2-2222-2-2-1-222-222-2-2111-1-1-11-2-2-2-22222-2222-2-21111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111000000000000000000003−3−33−333−300000000
χ642-2-2222-2-2-1-222-222-2-2111-1-1-11-2-2-2-22222-2222-2-21111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−333−33−3−3300000000
χ652-2-22-2-2222000-22-220-2-222-2-2222-2-2-2-222000000000000-22002-222-2-20000-2-222000000000000000000000000000000002−2−222−2−22
χ662-2-22-2-2222000-22-220-2-222-2-2222-2-2-2-222000000000000-22002-222-2-20000-2-22200000000000000000000000000000000−222−2−222−2
χ672-2-22-2-2222000-22-220-2-222-2-22-2-22222-2-2000000000000-22002-2-2-222000022-2-2000000000000000000000000000000002−2−22−222−2
χ682-2-22-2-2222000-22-220-2-222-2-22-2-22222-2-2000000000000-22002-2-2-222000022-2-200000000000000000000000000000000−222−22−2−22
χ6944444444-2444-4-4-4-44-2-2-2-2-2-2-200000000-4-40000-2-222-2-22222220000000000000000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-20000000044000022-2-22222-2-2220000000000000000000000000000000000000000000000000000
χ714444-4-4-4-44000-4-444044-44-4-4-400000000000000000000-4400-440000000000000000000000000000000000000000000000000000
χ724444-4-4-4-4-200044-4-40-2-22-222244-4-444-4-4000000000000-2200-22-2-2220000-2-2220000000000000000000000000000000000000000
χ734444-4-4-4-4-200044-4-40-2-22-2222-4-444-4-444000000000000-2200-2222-2-2000022-2-20000000000000000000000000000000000000000
χ744444-4-4-4-4-2000-4-4440-2-22-2222000000000000000000002-2002-20000−2i32i3−2i32i30000−2i32i3−2i32i3000000000000000000000000000000000000
χ754444-4-4-4-4-2000-4-4440-2-22-2222000000000000000000002-2002-200002i3−2i32i3−2i300002i3−2i32i3−2i3000000000000000000000000000000000000
χ7644-4-44-44-4-244-40000-4-22-22-22222−2222−2222−2222−220022−2222−22-2200-22000000−22−22−2−222−22−22−2−222000000000000000000000000000000000000
χ7744-4-44-44-4-244-40000-4-22-22-222−2222−2222−2222−222200−2222−2222-2200-220000002−22−222−2−22−22−222−2−2000000000000000000000000000000000000
χ7844-4-44-44-4-2-4-4400004-22-22-22222−2222−2222−2222−2200−2222−22222-2002-2000000−22−2222−2−2−22−2222−2−2000000000000000000000000000000000000
χ7944-4-44-44-4-2-4-4400004-22-22-222−2222−2222−2222−22220022−2222−222-2002-20000002−22−2−2−2222−22−2−2−222000000000000000000000000000000000000
χ8044-4-4-44-444000000004-4-4-4-44422−22−222222−22−222200000000000000000022−22−2222000022−22−22220000000000000000000000000000000000000000
χ8144-4-4-44-444000000004-4-4-4-444−222222−22−222222−22000000000000000000−222222−220000−222222−220000000000000000000000000000000000000000
χ8244-4-4-44-44-200000000-22222-2-222−22−222222−22−222200000000−2i32i30000−2i32i300−222−2i6−i6−i6i6−222−2i6−i6−i6i6000000000000000000000000000000000000
χ8344-4-4-44-44-200000000-22222-2-222−22−222222−22−2222000000002i3−2i300002i3−2i300−222−2−i6i6i6−i6−222−2−i6i6i6−i6000000000000000000000000000000000000
χ8444-4-4-44-44-200000000-22222-2-2−222222−22−222222−2200000000−2i32i30000−2i32i3002−2−22−i6i6i6−i62−2−22−i6i6i6−i6000000000000000000000000000000000000
χ8544-4-4-44-44-200000000-22222-2-2−222222−22−222222−22000000002i3−2i300002i3−2i3002−2−22i6−i6−i6i62−2−22i6−i6−i6i6000000000000000000000000000000000000
χ864-44-44-4-44-24-440000-42-222-22-222−2222−22−2222−22220022−22−2222-22002-2000000−22−22−2−2222−22−222−2−2000000000000000000000000000000000000
χ874-44-44-4-44-24-440000-42-222-22-2−2222−222222−2222−2200−222222−22-22002-20000002−22−222−2−2−22−22−2−222000000000000000000000000000000000000
χ884-44-44-4-44-2-44-4000042-222-22-222−2222−22−2222−222200−222222−222-200-22000000−22−2222−2−22−22−2−2−222000000000000000000000000000000000000
χ894-44-44-4-44-2-44-4000042-222-22-2−2222−222222−2222−220022−22−22222-200-220000002−22−2−2−222−22−2222−2−2000000000000000000000000000000000000
χ904-44-4-444-4400000000-444-4-44-422−22−2222−222222−2200000000000000000022−22−22220000−222222−220000000000000000000000000000000000000000
χ914-44-4-444-4400000000-444-4-44-4−222222−2222−22−2222000000000000000000−222222−22000022−22−22220000000000000000000000000000000000000000
χ924-44-4-444-4-2000000002-2-222-2222−22−2222−222222−2200000000−2i32i300002i3−2i300−222−2i6−i6−i6i62−2−22−i6i6i6−i6000000000000000000000000000000000000
χ934-44-4-444-4-2000000002-2-222-2222−22−2222−222222−22000000002i3−2i30000−2i32i300−222−2−i6i6i6−i62−2−22i6−i6−i6i6000000000000000000000000000000000000
χ944-44-4-444-4-2000000002-2-222-22−222222−2222−22−222200000000−2i32i300002i3−2i3002−2−22−i6i6i6−i6−222−2i6−i6−i6i6000000000000000000000000000000000000
χ954-44-4-444-4-2000000002-2-222-22−222222−2222−22−2222000000002i3−2i30000−2i32i3002−2−22i6−i6−i6i6−222−2−i6i6i6−i6000000000000000000000000000000000000
χ964-4-4444-4-4-24-4-44-4-444222-2-2-2200000000-440000-2-22222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ974-4-4444-4-4-2-4444-4-44-4222-2-2-22000000004-4000022-2-2-2-2-2-222220000000000000000000000000000000000000000000000000000
χ984-4-44-4-44440004-44-40-4-444-4-44000000000000000000004-400-440000000000000000000000000000000000000000000000000000
χ994-4-44-4-444-20004-44-4022-2-222-200000000000000000000-22002-20000−2i32i3−2i32i300002i3−2i32i3−2i3000000000000000000000000000000000000
χ1004-4-44-4-444-20004-44-4022-2-222-200000000000000000000-22002-200002i3−2i32i3−2i30000−2i32i3−2i32i3000000000000000000000000000000000000
χ1014-4-44-4-444-2000-44-44022-2-222-244-4-4-4-4440000000000002-200-22-2-222000022-2-20000000000000000000000000000000000000000
χ1024-4-44-4-444-2000-44-44022-2-222-2-4-44444-4-40000000000002-200-2222-2-20000-2-2220000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).