Finite Group Databasebeta

← Group #10742705

Character table — Group #10742705

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111111111111122222222222222224444444488888888888888888888888888888888888888121212121212121212121212121212122424242424242424
order122222222222222236666666666666662222444444444444446666121212121212121212121212121212121212121212121212222222222222444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-111-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ911111111111111111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1
χ1011111111111111111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ1111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ1211111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-1
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ172222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ182222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000000000000
χ192222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000000000000000
χ202222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-1000000000000000000000000
χ212222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-222-2-222-2-21111-1-1-1-11111-1-1-1-11111-1-1-1-11111000000000000000000000000
χ222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-222-2-2221111-1-1-1-111111111-1-1-1-11111-1-1-1-1000000000000000000000000
χ232222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-22211111111-1-1-1-1-1-1-1-111111111-1-1-1-1000000000000000000000000
χ242222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-22222-2-211111111-1-1-1-11111-1-1-1-1-1-1-1-11111000000000000000000000000
χ2522222-2-222-2-2-22-2-2-2222222-2-2-2-222-2-2-2-2000000000000002i−2i00000000000000000000002i2i−2i−2i000022-2-2000000002i2i−2i−2i00000000
χ2622222-2-222-2-2-22-2-2-2222222-2-2-2-222-2-2-2-2000000000000002i−2i00000000000000000000002i2i−2i−2i0000-2-22200000000−2i−2i2i2i00000000
χ2722222-2-222-2-2-22-2-2-2222222-2-2-2-222-2-2-2-200000000000000−2i2i0000000000000000000000−2i−2i2i2i000022-2-200000000−2i−2i2i2i00000000
χ2822222-2-222-2-2-22-2-2-2222222-2-2-2-222-2-2-2-200000000000000−2i2i0000000000000000000000−2i−2i2i2i0000-2-222000000002i2i−2i−2i00000000
χ292222-22-2-2-222-2-22-2-22222-2-222-2-2-2-222-2-200002i2i−2i−2i000000000000002i2i−2i−2i00000000000000000000000022-2-200000000002i−2i0000
χ302222-22-2-2-222-2-22-2-22222-2-222-2-2-2-222-2-200002i2i−2i−2i000000000000002i2i−2i−2i000000000000000000000000-2-2220000000000−2i2i0000
χ312222-22-2-2-222-2-22-2-22222-2-222-2-2-2-222-2-20000−2i−2i2i2i00000000000000−2i−2i2i2i00000000000000000000000022-2-20000000000−2i2i0000
χ322222-22-2-2-222-2-22-2-22222-2-222-2-2-2-222-2-20000−2i−2i2i2i00000000000000−2i−2i2i2i000000000000000000000000-2-22200000000002i−2i0000
χ3322-2-22222-22-2-2-2-22-222-2-22-22-2222-22-2-2-200000000000000002i−2i0000000000000000000000002i2i−2i−2i00002-22-200002i−2i2i−2i00000000
χ3422-2-22222-22-2-2-2-22-222-2-22-22-2222-22-2-2-200000000000000002i−2i0000000000000000000000002i2i−2i−2i0000-22-220000−2i2i−2i2i00000000
χ3522-2-22222-22-2-2-2-22-222-2-22-22-2222-22-2-2-20000000000000000−2i2i000000000000000000000000−2i−2i2i2i00002-22-20000−2i2i−2i2i00000000
χ3622-2-22222-22-2-2-2-22-222-2-22-22-2222-22-2-2-20000000000000000−2i2i000000000000000000000000−2i−2i2i2i0000-22-2200002i−2i2i−2i00000000
χ3722-2-22-2-22-2-222-22-2222-2-22-2-22-2-22-2-222222-2-20000000000000022-2-20000000000000000000000000000000000002-2-2200002-200
χ3822-2-22-2-22-2-222-22-2222-2-22-2-22-2-22-2-222222-2-20000000000000022-2-2000000000000000000000000000000000000-222-20000-2200
χ3922-2-22-2-22-2-222-22-2222-2-22-2-22-2-22-2-2222-2-22200000000000000-2-2220000000000000000000000000000000000002-2-220000-2200
χ4022-2-22-2-22-2-222-22-2222-2-22-2-22-2-22-2-2222-2-22200000000000000-2-222000000000000000000000000000000000000-222-200002-200
χ4122-2-2-22-2-222-222-2-2222-2-2-222-2-2-2-222-2220000000000002-20000000000000000000022-2-20000000000002-2-2222-2-2000000000000
χ4222-2-2-22-2-222-222-2-2222-2-2-222-2-2-2-222-2220000000000002-20000000000000000000022-2-2000000000000-222-2-2-222000000000000
χ4322-2-2-22-2-222-222-2-2222-2-2-222-2-2-2-222-222000000000000-2200000000000000000000-2-2220000000000002-2-22-2-222000000000000
χ4422-2-2-22-2-222-222-2-2222-2-2-222-2-2-2-222-222000000000000-2200000000000000000000-2-222000000000000-222-222-2-2000000000000
χ452-22-2222-22-2-22-22-2-22-22-22-2222-2-22-2-22-200002i−2i2i−2i000000000000002i−2i2i−2i000000000000000000002-22-20000000000002i−2i000000
χ462-22-2222-22-2-22-22-2-22-22-22-2222-2-22-2-22-200002i−2i2i−2i000000000000002i−2i2i−2i00000000000000000000-22-22000000000000−2i2i000000
χ472-22-2222-22-2-22-22-2-22-22-22-2222-2-22-2-22-20000−2i2i−2i2i00000000000000−2i2i−2i2i000000000000000000002-22-2000000000000−2i2i000000
χ482-22-2222-22-2-22-22-2-22-22-22-2222-2-22-2-22-20000−2i2i−2i2i00000000000000−2i2i−2i2i00000000000000000000-22-220000000000002i−2i000000
χ492-22-22-2-2-2222-2-2-2222-22-22-2-2-2-22-2222-2200000000002-200000000000000000022-2-20000000000002-2-2200002-22-2000000000000
χ502-22-22-2-2-2222-2-2-2222-22-22-2-2-2-22-2222-2200000000002-200000000000000000022-2-2000000000000-222-20000-22-22000000000000
χ512-22-22-2-2-2222-2-2-2222-22-22-2-2-2-22-2222-220000000000-22000000000000000000-2-2220000000000002-2-220000-22-22000000000000
χ522-22-22-2-2-2222-2-2-2222-22-22-2-2-2-22-2222-220000000000-22000000000000000000-2-222000000000000-222-200002-22-2000000000000
χ532-22-2-22-22-2-2-2-222222-22-2-2222-222-2-2-2-222-22-22-2-222-2000000002-22-22-2-2222-2-20000000000000000000000000000000000000000
χ542-22-2-22-22-2-2-2-222222-22-2-2222-222-2-2-2-222-22-2-222-2-22000000002-22-2-222-2-2-2220000000000000000000000000000000000000000
χ552-22-2-22-22-2-2-2-222222-22-2-2222-222-2-2-2-22-22-222-2-22-2200000000-22-222-2-22-2-2220000000000000000000000000000000000000000
χ562-22-2-22-22-2-2-2-222222-22-2-2222-222-2-2-2-22-22-22-222-22-200000000-22-22-222-222-2-20000000000000000000000000000000000000000
χ572-22-2-22-22-2-2-2-22222-11-111-1-1-11-1-11111-12-22-22-2-222-200000000-11-11-111-1-1-1113−33−33−33−33−33−33−33−3000000000000000000000000
χ582-22-2-22-22-2-2-2-22222-11-111-1-1-11-1-11111-12-22-22-2-222-200000000-11-11-111-1-1-111−33−33−33−33−33−33−33−33000000000000000000000000
χ592-22-2-22-22-2-2-2-22222-11-111-1-1-11-1-11111-12-22-2-222-2-2200000000-11-111-1-1111-1-13−33−33−33−3−33−33−33−33000000000000000000000000
χ602-22-2-22-22-2-2-2-22222-11-111-1-1-11-1-11111-12-22-2-222-2-2200000000-11-111-1-1111-1-1−33−33−33−333−33−33−33−3000000000000000000000000
χ612-22-2-22-22-2-2-2-22222-11-111-1-1-11-1-11111-1-22-222-2-22-22000000001-11-1-111-111-1-13−33−3−33−333−33−3−33−33000000000000000000000000
χ622-22-2-22-22-2-2-2-22222-11-111-1-1-11-1-11111-1-22-222-2-22-22000000001-11-1-111-111-1-1−33−333−33−3−33−333−33−3000000000000000000000000
χ632-22-2-22-22-2-2-2-22222-11-111-1-1-11-1-11111-1-22-22-222-22-2000000001-11-11-1-11-1-1113−33−3−33−33−33−333−33−3000000000000000000000000
χ642-22-2-22-22-2-2-2-22222-11-111-1-1-11-1-11111-1-22-22-222-22-2000000001-11-11-1-11-1-111−33−333−33−33−33−3−33−33000000000000000000000000
χ652-2-22-2-22222-2-2-22-222-2-22-2-2-222-2222-2-222-2-22000000000000002-2-22000000000000000000000000000000002-2-2200000000002-2
χ662-2-22-2-22222-2-2-22-222-2-22-2-2-222-2222-2-222-2-22000000000000002-2-2200000000000000000000000000000000-222-20000000000-22
χ672-2-22-2-22222-2-2-22-222-2-22-2-2-222-2222-2-22-222-200000000000000-222-2000000000000000000000000000000002-2-220000000000-22
χ682-2-22-2-22222-2-2-22-222-2-22-2-2-222-2222-2-22-222-200000000000000-222-200000000000000000000000000000000-222-200000000002-2
χ6944444-4-444-4-4-44-4-4-4-2-2-2-2-2-22222-2-22222000000000000004i−4i0000000000000000000000−2i−2i2i2i0000000000000000000000000000
χ7044444-4-444-4-4-44-4-4-4-2-2-2-2-2-22222-2-2222200000000000000−4i4i00000000000000000000002i2i−2i−2i0000000000000000000000000000
χ714444-44-4-4-444-4-44-4-4-2-2-2-222-2-22222-2-22200004i4i−4i−4i00000000000000−2i−2i2i2i00000000000000000000000000000000000000000000
χ724444-44-4-4-444-4-44-4-4-2-2-2-222-2-22222-2-2220000−4i−4i4i4i000000000000002i2i−2i−2i00000000000000000000000000000000000000000000
χ734444-4-44-4-4-4-44-4-4444444-4-4-4-444-4-4-4-4440000000000000000000000000000000000000000000000000000000000000000000000
χ744444-4-44-4-4-4-44-4-444-2-2-2-22222-2-22222-2-200000000000000000000000000000023−23−2323000000000000000000000000000000000000
χ754444-4-44-4-4-4-44-4-444-2-2-2-22222-2-22222-2-2000000000000000000000000000000−232323−23000000000000000000000000000000000000
χ7644-4-44444-44-4-4-4-44-4-2-222-22-22-2-2-22-222200000000000000004i−4i000000000000000000000000−2i−2i2i2i000000000000000000000000
χ7744-4-44444-44-4-4-4-44-4-2-222-22-22-2-2-22-22220000000000000000−4i4i0000000000000000000000002i2i−2i−2i000000000000000000000000
χ7844-4-44-4-44-4-444-44-44-2-222-222-222-222-2-2-244-4-400000000000000-2-222000000000000000000000000000000000000000000000000
χ7944-4-44-4-44-4-444-44-44-2-222-222-222-222-2-2-2-4-4440000000000000022-2-2000000000000000000000000000000000000000000000000
χ8044-4-4-44-4-444-444-4-44-2-2222-2-22222-2-22-2-20000000000004-400000000000000000000-2-22200000000000000000000000000000000
χ8144-4-4-44-4-444-444-4-44-2-2222-2-22222-2-22-2-2000000000000-440000000000000000000022-2-200000000000000000000000000000000
χ8244-4-4-4-44-44-44-4444-444-4-4-44-4444-44-44-4-40000000000000000000000000000000000000000000000000000000000000000000000
χ8344-4-4-4-44-44-44-4444-4-2-2222-22-2-2-22-22-2220000000000000000000000000023−2323−230000000000000000000000000000000000000000
χ8444-4-4-4-44-44-44-4444-4-2-2222-22-2-2-22-22-22200000000000000000000000000−2323−23230000000000000000000000000000000000000000
χ854-44-4444-44-4-44-44-4-4-22-22-22-2-2-222-222-2200004i−4i4i−4i00000000000000−2i2i−2i2i00000000000000000000000000000000000000000000
χ864-44-4444-44-4-44-44-4-4-22-22-22-2-2-222-222-220000−4i4i−4i4i000000000000002i−2i2i−2i00000000000000000000000000000000000000000000
χ874-44-44-4-4-4444-4-4-444-22-22-22222-22-2-2-22-200000000004-4000000000000000000-2-222000000000000000000000000000000000000
χ884-44-44-4-4-4444-4-4-444-22-22-22222-22-2-2-22-20000000000-4400000000000000000022-2-2000000000000000000000000000000000000
χ894-44-4-4-444-44444-4-4-44-44-4-44-4-44-44-4444-40000000000000000000000000000000000000000000000000000000000000000000000
χ904-44-4-4-444-44444-4-4-4-22-222-222-22-22-2-2-2200000000000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000
χ914-44-4-4-444-44444-4-4-4-22-222-222-22-22-2-2-22000000000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000
χ924-4-44444-4-4-44-44-4-444-4-44444-44-4-4-4-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ934-4-44444-4-4-44-44-4-44-222-2-2-2-22-22222-22-2000000000000000000000000000000000023−23−232300000000000000000000000000000000
χ944-4-44444-4-4-44-44-4-44-222-2-2-2-22-22222-22-20000000000000000000000000000000000−232323−2300000000000000000000000000000000
χ954-4-444-4-4-4-44-44444-44-4-4444-44-44-4-44-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ964-4-444-4-4-4-44-44444-4-222-2-2-22-22-222-22-220000000000000000000000000023−23−23230000000000000000000000000000000000000000
χ974-4-444-4-4-4-44-44444-4-222-2-2-22-22-222-22-2200000000000000000000000000−232323−230000000000000000000000000000000000000000
χ984-4-44-44-444-444-4-44-44-4-44-4-44-4-4444-444-40000000000000000000000000000000000000000000000000000000000000000000000
χ994-4-44-44-444-444-4-44-4-222-222-222-2-2-22-2-22000000000000000000000000000000000000000000−2i32i32i3−2i3000000000000000000000000
χ1004-4-44-44-444-444-4-44-4-222-222-222-2-2-22-2-220000000000000000000000000000000000000000002i3−2i3−2i32i3000000000000000000000000
χ1014-4-44-4-44444-4-4-44-44-222-2222-2-22-2-2-222-24-4-4400000000000000-222-2000000000000000000000000000000000000000000000000
χ1024-4-44-4-44444-4-4-44-44-222-2222-2-22-2-2-222-2-444-4000000000000002-2-22000000000000000000000000000000000000000000000000

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