Finite Group Databasebeta

← Group #10691331

Character table — Group #10691331

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order122222223444444446666666444444444412121212121212128888888888881212121212121212121224242424242424248888888888884412121212888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ7111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ91-1-1-111-111111-1-1-11-1-1-1-1111-111-1-11-111-1-111-1-111-1-1iiii−i−i−i−iii−i−i1-11111-1-1-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−ii−iii−i−i11-1-11-1
χ101-1-1-111-111111-1-1-11-1-1-1-1111-111-1-11-111-1-111-1-111-1-1iiii−i−i−i−i−i−iii1-11111-1-1-1-1−i−i−i−iiiiiii−i−iiiii−i−i−i−i−ii−i−iii-1-111-11
χ111-1-1-111-111111-1-1-11-1-1-1-1111-111-1-11-111-1-111-1-111-1-1−i−i−i−iiiiiii−i−i1-11111-1-1-1-1iiii−i−i−i−i−i−iii−i−i−i−iiiiii−iii−i−i-1-111-11
χ121-1-1-111-111111-1-1-11-1-1-1-1111-111-1-11-111-1-111-1-111-1-1−i−i−i−iiiii−i−iii1-11111-1-1-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii−ii−i−iii11-1-11-1
χ131-1-1-111-111111-1-1-11-1-1-1-1111-1-1-1111-1-1-11111-1-111-1-1iiii−i−i−i−iii−i−i1-1-1-1-1-11111iiii−i−i−i−iii−i−i−i−i−i−iiiii−ii−i−iii11-1-1-11
χ141-1-1-111-111111-1-1-11-1-1-1-1111-1-1-1111-1-1-11111-1-111-1-1iiii−i−i−i−i−i−iii1-1-1-1-1-11111−i−i−i−iiiiiii−i−i−i−i−i−iiiiii−iii−i−i-1-1111-1
χ151-1-1-111-111111-1-1-11-1-1-1-1111-1-1-1111-1-1-11111-1-111-1-1−i−i−i−iiiiiii−i−i1-1-1-1-1-11111iiii−i−i−i−i−i−iiiiiii−i−i−i−i−ii−i−iii-1-1111-1
χ161-1-1-111-111111-1-1-11-1-1-1-1111-1-1-1111-1-1-11111-1-111-1-1−i−i−i−iiiii−i−iii1-1-1-1-1-11111−i−i−i−iiiii−i−iiiiiii−i−i−i−ii−iii−i−i11-1-1-11
χ1722222222222-2-2-22-2222222220000-2-200002222-2-2-2-2222222220000-2-20000000000000000-2-2-2-200000000000000000000
χ1822222222222-2-2-22-2222222220000-2-200002222-2-2-2-2-2-2-2-2-2-2-2-20000-2-20000000000000000222200000000000000000000
χ19222222222-2-2222-22-222222222222-2-2-2-2-2-2-2-2-2-22222000000000000-2-222-2-222-2-200000000000000000000000000000000
χ20222222222-2-2222-22-22222222-2-2-2-2-2-22222-2-2-2-22222000000000000-2-2-2-222-2-22200000000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-222222220000220000-2-2-2-2-2-2-2-200000000000022000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ22222222222-2-2-2-2-2-2-2-222222220000220000-2-2-2-2-2-2-2-20000000000002200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2322222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ2422222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ2522222222-122222222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1000000002222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ2622222222-122222222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1111111111111111100000000000022-1-1-1-1000000
χ2722222222-1-2-2222-22-2-1-1-1-1-1-1-12222-2-2-2-2-2-21111-1-1-1-100000000000011-1-111-1-111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i3000000
χ2822222222-1-2-2222-22-2-1-1-1-1-1-1-12222-2-2-2-2-2-21111-1-1-1-100000000000011-1-111-1-111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i3000000
χ2922222222-1-2-2222-22-2-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-10000000000001111-1-111-1-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i3000000
χ3022222222-1-2-2222-22-2-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-10000000000001111-1-111-1-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i3000000
χ31222-22-2-2-222-200020-222-22-2-2-200000000002-22-2000022-2-222-2-22−22−200000000002−22−22−22−20000000000000000002−22−200
χ32222-22-2-2-222-200020-222-22-2-2-200000000002-22-2000022-2-222-2-2−22−220000000000−22−22−22−22000000000000000000−22−2200
χ33222-22-2-2-222-200020-222-22-2-2-200000000002-22-20000-2-222-2-2222−22−200000000002−22−22−22−2000000000000000000−22−2200
χ34222-22-2-2-222-200020-222-22-2-2-200000000002-22-20000-2-222-2-222−22−220000000000−22−22−22−220000000000000000002−22−200
χ3522-22-22-2-220022-20-202-22-22-2-22-22-200000000002-22-22−22−22−22−20000002-2002-200000000002−22−22−22−22−22−2000000000000
χ3622-22-22-2-220022-20-202-22-22-2-22-22-200000000002-22-2−22−22−22−220000002-2002-20000000000−22−22−22−22−22−22000000000000
χ3722-22-22-2-220022-20-202-22-22-2-2-22-2200000000002-22-22−22−22−22−2000000-2200-2200000000002−22−2−22−22−22−22000000000000
χ3822-22-22-2-220022-20-202-22-22-2-2-22-2200000000002-22-2−22−22−22−22000000-2200-220000000000−22−222−22−22−22−2000000000000
χ3922-22-22-2-2200-2-220202-22-22-2-20000002i−2i2i−2i0000-22-222−22−22−22−2000000002i−2i002i−2i00000000−22−22−i2i2i2−i2−i2i2i2−i2000000000000
χ4022-22-22-2-2200-2-220202-22-22-2-20000002i−2i2i−2i0000-22-22−22−22−22−22000000002i−2i002i−2i000000002−22−2i2−i2−i2i2i2−i2−i2i2000000000000
χ4122-22-22-2-2200-2-220202-22-22-2-2000000−2i2i−2i2i0000-22-222−22−22−22−200000000−2i2i00−2i2i00000000−22−22i2−i2−i2i2i2−i2−i2i2000000000000
χ4222-22-22-2-2200-2-220202-22-22-2-2000000−2i2i−2i2i0000-22-22−22−22−22−2200000000−2i2i00−2i2i000000002−22−2−i2i2i2−i2−i2i2i2−i2000000000000
χ432-22-2-222-22002-220-20-22-2-22-222-2-2200000000002-2-22−i2i2−i2i2i2−i2i2−i20000002-200-220000000000−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ442-22-2-222-22002-220-20-22-2-22-222-2-2200000000002-2-22i2−i2i2−i2−i2i2−i2i20000002-200-220000000000i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ452-22-2-222-22002-220-20-22-2-22-22-222-200000000002-2-22−i2i2−i2i2i2−i2i2−i2000000-22002-20000000000−i2i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ462-22-2-222-22002-220-20-22-2-22-22-222-200000000002-2-22i2−i2i2−i2−i2i2−i2i2000000-22002-20000000000i2−i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ472-22-2-222-2200-22-2020-22-2-22-220000002i−2i−2i2i0000-222-2−i2i2−i2i2i2−i2i2−i2000000002i−2i00−2i2i00000000i2−i2−i2i2−222−22−2−22000000000000
χ482-22-2-222-2200-22-2020-22-2-22-220000002i−2i−2i2i0000-222-2i2−i2i2−i2−i2i2−i2i2000000002i−2i00−2i2i00000000−i2i2i2−i22−2−22−222−2000000000000
χ492-22-2-222-2200-22-2020-22-2-22-22000000−2i2i2i−2i0000-222-2−i2i2−i2i2i2−i2i2−i200000000−2i2i002i−2i00000000i2−i2−i2i22−2−22−222−2000000000000
χ502-22-2-222-2200-22-2020-22-2-22-22000000−2i2i2i−2i0000-222-2i2−i2i2−i2−i2i2−i2i200000000−2i2i002i−2i00000000−i2i2i2−i2−222−22−2−22000000000000
χ512-2-222-22-222-2000-202-2-222-2-2200000000002-2-2200002i2i−2i−2i−2i−2i2i2i−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2000000000000000000−222−200
χ522-2-222-22-222-2000-202-2-222-2-2200000000002-2-2200002i2i−2i−2i−2i−2i2i2ii2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i20000000000000000002−2−2200
χ532-2-222-22-222-2000-202-2-222-2-2200000000002-2-220000−2i−2i2i2i2i2i−2i−2i−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i20000000000000000002−2−2200
χ542-2-222-22-222-2000-202-2-222-2-2200000000002-2-220000−2i−2i2i2i2i2i−2i−2ii2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000000000−222−200
χ552-2-2-222-22222-222-2-2-2-2-2-2222-20000-22000022-2-2-2-2222i2i2i2i−2i−2i−2i−2i0000-220000000000000000−2i−2i2i2i00000000000000000000
χ562-2-2-222-22222-222-2-2-2-2-2-2222-20000-22000022-2-2-2-222−2i−2i−2i−2i2i2i2i2i0000-2200000000000000002i2i−2i−2i00000000000000000000
χ572-2-2-222-222-2-22-2-2222-2-2-2222-222-2-2-22-2-222-2-22222-2-2000000000000-2222-2-2-2-22200000000000000000000000000000000
χ582-2-2-222-222-2-22-2-2222-2-2-2222-2-2-222-2222-2-2-2-22222-2-2000000000000-22-2-22222-2-200000000000000000000000000000000
χ592-2-2-222-222-2-2-2222-22-2-2-2222-200002-20000-2-222-2-2220000000000002-20000000000000000000022-2-2-2-222000000000000
χ602-2-2-222-222-2-2-2222-22-2-2-2222-200002-20000-2-222-2-2220000000000002-200000000000000000000-2-22222-2-2000000000000
χ612-2-2-222-22-1222-2-2-22-2111-1-1-1122-2-22-222-2-2-1-111-1-111000000002i2i−2i−2i-11-1-1-1-11111−i−i−i−iiiii0000000000002i−2i−i−iii000000
χ622-2-2-222-22-1222-2-2-22-2111-1-1-1122-2-22-222-2-2-1-111-1-11100000000−2i−2i2i2i-11-1-1-1-11111iiii−i−i−i−i000000000000−2i2iii−i−i000000
χ632-2-2-222-22-1222-2-2-22-2111-1-1-11-2-2222-2-2-222-1-111-1-111000000002i2i−2i−2i-111111-1-1-1-1−i−i−i−iiiii000000000000−2i2iii−i−i000000
χ642-2-2-222-22-1222-2-2-22-2111-1-1-11-2-2222-2-2-222-1-111-1-11100000000−2i−2i2i2i-111111-1-1-1-1iiii−i−i−i−i0000000000002i−2i−i−iii000000
χ652-2-2-222-22-1-2-22-2-2222111-1-1-1122-2-2-22-2-22211-1-1-1-1110000000000001-1-1-11111-1-133−3−3−3−333000000000000003−3−33000000
χ662-2-2-222-22-1-2-22-2-2222111-1-1-1122-2-2-22-2-22211-1-1-1-1110000000000001-1-1-11111-1-1−3−33333−3−300000000000000−333−3000000
χ672-2-2-222-22-1-2-22-2-2222111-1-1-11-2-222-2222-2-211-1-1-1-1110000000000001-111-1-1-1-11133−3−3−3−33300000000000000−333−3000000
χ682-2-2-222-22-1-2-22-2-2222111-1-1-11-2-222-2222-2-211-1-1-1-1110000000000001-111-1-1-1-111−3−33333−3−3000000000000003−3−33000000
χ6944444444-244-4-4-44-44-2-2-2-2-2-2-20000-4-40000-2-2-2-22222000000000000220000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2000044000022222222000000000000-2-20000000000000000000000000000000000000000
χ71444-44-4-4-44-44000-40444-44-4-4-40000000000-44-440000000000000000000000000000000000000000000000000000000000
χ72444-44-4-4-4-24-400040-4-2-22-22220000000000-22-2200000000000022−2222−220000000000−22−22−22−22000000000000000000000000
χ73444-44-4-4-4-24-400040-4-2-22-22220000000000-22-22000000000000−2222−222200000000002−22−22−22−2000000000000000000000000
χ74444-44-4-4-4-2-44000-404-2-22-222200000000002-22-200000000000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ75444-44-4-4-4-2-44000-404-2-22-222200000000002-22-200000000000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ7644-44-44-4-4-20044-40-40-22-22-2224-44-40000000000-22-2200000000000000-2200-220000000000000000000000000000000000
χ7744-44-44-4-4-20044-40-40-22-22-222-44-440000000000-22-22000000000000002-2002-20000000000000000000000000000000000
χ7844-44-44-4-4-200-4-44040-22-22-2220000004i−4i4i−4i00002-22-20000000000000000−2i2i00−2i2i00000000000000000000000000000000
χ7944-44-44-4-4-200-4-44040-22-22-222000000−4i4i−4i4i00002-22-200000000000000002i−2i002i−2i00000000000000000000000000000000
χ8044-4-4-4-4444000000004-4-4-4-44400000000000000000022−22−222222−22−22220000000000000000000000000000000000000000000000
χ8144-4-4-4-4444000000004-4-4-4-444000000000000000000−222222−22−222222−220000000000000000000000000000000000000000000000
χ824-444-4-4-44400000000-444-4-44-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ834-444-4-4-44400000000-444-4-44-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ844-44-4-444-4-2004-440-402-222-22-24-4-440000000000-222-200000000000000-22002-20000000000000000000000000000000000
χ854-44-4-444-4-2004-440-402-222-22-2-444-40000000000-222-2000000000000002-200-220000000000000000000000000000000000
χ864-44-4-444-4-200-44-40402-222-22-20000004i−4i−4i4i00002-2-220000000000000000−2i2i002i−2i00000000000000000000000000000000
χ874-44-4-444-4-200-44-40402-222-22-2000000−4i4i4i−4i00002-2-2200000000000000002i−2i00−2i2i00000000000000000000000000000000
χ884-4-444-44-44-4400040-4-4-444-4-440000000000-444-40000000000000000000000000000000000000000000000000000000000
χ894-4-444-44-4-24-4000-40422-2-222-20000000000-222-2000000000000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ904-4-444-44-4-24-4000-40422-2-222-20000000000-222-20000000000002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ914-4-444-44-4-2-4400040-422-2-222-200000000002-2-22000000000000000000000000006−6−66−666−6000000000000000000000000
χ924-4-444-44-4-2-4400040-422-2-222-200000000002-2-2200000000000000000000000000−666−66−6−66000000000000000000000000
χ934-4-4-444-44-244-444-4-4-4222-2-2-220000-440000-2-22222-2-20000000000002-20000000000000000000000000000000000000000
χ944-4-4-444-44-2-4-4-4444-44222-2-2-2200004-4000022-2-222-2-2000000000000-220000000000000000000000000000000000000000
χ9588-8-8-8-888-400000000-44444-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ968-888-8-8-88-4000000004-4-444-44000000000000000000000000000000000000000000000000000000000000000000000000

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