Finite Group Databasebeta

← Group #10876305

Character table — Group #10876305

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order12442223444612124444666121212121212122488888812122424242424242424224446812121224242424244488888848
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-11-11-1-111-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-11-111-1-111-1-111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11111-1-1111111-1-1
χ911111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1111111-1111-1-1-1-111-1-1-1-1-1-1111-1
χ1011111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1111-1-1-1-1-1-1111111-1-1-11
χ1111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1111-1-1-1-11111-1-1-1-111-1-1-11
χ1211111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1111-1-1-1-111-1-11111-1-1111-1
χ1311111111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-11-1-1-11111-1-1-1-111-1-111-11
χ1411111111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-111111111-1-111-1-11-1
χ1511111111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-1111111111-1-1-11111-1-1-1-1-1-11111-1-11-1
χ1611111111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-11111-1-11111-1-1-1-111-11
χ172222222-1222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-100002-12-1-1-1-1-1-1-1000000000000
χ182222222-1222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-2-1-2-111-1-111000000000000
χ192222222-1222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-10000-21-21111111000000000000
χ202222222-1222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111111100002121-1-111-1-1000000000000
χ212222222-1222-1-1-1-2-2-2-2-1-1-1-11111-1-122-2-222-2-211-1-1-1-1111100002-1-2-1-1-11111000000000000
χ222222222-1222-1-1-1-2-2-2-2-1-1-1-11111-1-122-2-2-2-222111111-1-1-1-10000-2-12-11111-1-1000000000000
χ232222222-1222-1-1-1-2-2-2-2-1-1-1-11111-1-1-2-22222-2-211-1-1-1-111110000-212111-1-1-1-1000000000000
χ242222222-1222-1-1-1-2-2-2-2-1-1-1-11111-1-1-2-222-2-222111111-1-1-1-1000021-21-1-1-1-111000000000000
χ252222-2-222-2-2222222-2-2-22-2-222222-200000000-2-2000000002-22-20000000000002-200000000
χ262222-2-222-2-2222222-2-2-22-2-222222-200000000-2-200000000-22-22000000000000-2200000000
χ272222-2-222-2-22222-2-222-22-2-2-2-2-2-22-20000000022000000002-22-2000000000000-2200000000
χ282222-2-222-2-22222-2-222-22-2-2-2-2-2-22-2000000002200000000-22-220000000000002-200000000
χ2922-2-22222-2-2-22-2-20000222-20000-2-20000002i−2i0000002i2i−2i−2i2-2-2200000000000000002i−2i0000
χ3022-2-22222-2-2-22-2-20000222-20000-2-20000002i−2i0000002i2i−2i−2i-222-20000000000000000−2i2i0000
χ3122-2-22222-2-2-22-2-20000222-20000-2-2000000−2i2i000000−2i−2i2i2i2-2-220000000000000000−2i2i0000
χ3222-2-22222-2-2-22-2-20000222-20000-2-2000000−2i2i000000−2i−2i2i2i-222-200000000000000002i−2i0000
χ3322-2-22-2-22-2222-2-22i−2i2i−2i-2-2222i2i−2i−2i2-2000000002i−2i00000000000000000000002-2002i−2i000000
χ3422-2-22-2-22-2222-2-22i−2i2i−2i-2-2222i2i−2i−2i2-2000000002i−2i0000000000000000000000-2200−2i2i000000
χ3522-2-22-2-22-2222-2-2−2i2i−2i2i-2-222−2i−2i2i2i2-200000000−2i2i00000000000000000000002-200−2i2i000000
χ3622-2-22-2-22-2222-2-2−2i2i−2i2i-2-222−2i−2i2i2i2-200000000−2i2i0000000000000000000000-22002i−2i000000
χ3722-2-2-22-222-222-2-22i−2i−2i2i2-2-2-22i2i−2i−2i222-22i−2i0000−2i2i000000000000020-2002i−2i00000000000000
χ3822-2-2-22-222-222-2-22i−2i−2i2i2-2-2-22i2i−2i−2i22-22−2i2i0000−2i2i0000000000000-20200−2i2i00000000000000
χ3922-2-2-22-222-222-2-2−2i2i2i−2i2-2-2-2−2i−2i2i2i222-2−2i2i00002i−2i000000000000020-200−2i2i00000000000000
χ4022-2-2-22-222-222-2-2−2i2i2i−2i2-2-2-2−2i−2i2i2i22-222i−2i00002i−2i0000000000000-202002i−2i00000000000000
χ4122-2-2-22-2-12-22-1112i−2i−2i2i-1111−i−iii-1-12-22i−2i0000i−i33−3−3−i3i3−i3i300000-1013−3−ii−i3i3000000000000
χ4222-2-2-22-2-12-22-1112i−2i−2i2i-1111−i−iii-1-12-22i−2i0000i−i−3−333i3−i3i3−i300000-101−33−iii3−i3000000000000
χ4322-2-2-22-2-12-22-1112i−2i−2i2i-1111−i−iii-1-1-22−2i2i0000i−i33−3−3−i3i3−i3i30000010-1−33i−ii3−i3000000000000
χ4422-2-2-22-2-12-22-1112i−2i−2i2i-1111−i−iii-1-1-22−2i2i0000i−i−3−333i3−i3i3−i30000010-13−3i−i−i3i3000000000000
χ4522-2-2-22-2-12-22-111−2i2i2i−2i-1111ii−i−i-1-12-2−2i2i0000−ii33−3−3i3−i3i3−i300000-1013−3i−ii3−i3000000000000
χ4622-2-2-22-2-12-22-111−2i2i2i−2i-1111ii−i−i-1-12-2−2i2i0000−ii−3−333−i3i3−i3i300000-101−33i−i−i3i3000000000000
χ4722-2-2-22-2-12-22-111−2i2i2i−2i-1111ii−i−i-1-1-222i−2i0000−ii33−3−3i3−i3i3−i30000010-1−33−ii−i3i3000000000000
χ4822-2-2-22-2-12-22-111−2i2i2i−2i-1111ii−i−i-1-1-222i−2i0000−ii−3−333−i3i3−i3i30000010-13−3−iii3−i3000000000000
χ4922-2-2-2-22222-22-2-20000-22-220000-2200002i−2i00002i−2i2i−2i000022-2-20000000000000000002i−2i00
χ5022-2-2-2-22222-22-2-20000-22-220000-2200002i−2i00002i−2i2i−2i0000-2-222000000000000000000−2i2i00
χ5122-2-2-2-22222-22-2-20000-22-220000-220000−2i2i0000−2i2i−2i2i000022-2-2000000000000000000−2i2i00
χ5222-2-2-2-22222-22-2-20000-22-220000-220000−2i2i0000−2i2i−2i2i0000-2-2220000000000000000002i−2i00
χ5344444-4-444-4-44440000-4-44-40000-4400000000000000000000000000000000000000000000
χ5444444-4-4-24-4-4-2-2-2000022-2200002-20000000000−2i32i32i3−2i3000000000000000000000000000000
χ5544444-4-4-24-4-4-2-2-2000022-2200002-200000000002i3−2i3−2i32i3000000000000000000000000000000
χ564444-44-44-44-444400004-4-440000-4-400000000000000000000000000000000000000000000
χ574444-44-4-2-44-4-2-2-20000-222-20000220000000000000023−23−232300000000000000000000000000
χ584444-44-4-2-44-4-2-2-20000-222-200002200000000000000−232323−2300000000000000000000000000
χ594444-4-44-2-4-44-2-2-244-4-42-222-2-2-2-2-2200000000220000000000000000000000000000000000
χ604444-4-44-2-4-44-2-2-2-4-4442-2222222-2200000000-2-20000000000000000000000000000000000
χ6144-4-4444-2-4-4-4-2220000-2-2-220000220000004i−4i000000−2i−2i2i2i00000000000000000000000000
χ6244-4-4444-2-4-4-4-2220000-2-2-22000022000000−4i4i0000002i2i−2i−2i00000000000000000000000000
χ6344-4-44-4-4-2-444-2224i−4i4i−4i22-2-2−2i−2i2i2i-2200000000−2i2i0000000000000000000000000000000000
χ6444-4-44-4-4-2-444-222−4i4i−4i4i22-2-22i2i−2i−2i-22000000002i−2i0000000000000000000000000000000000
χ6544-4-4-4-44-244-4-22200002-22-200002-200004i−4i0000−2i2i−2i2i000000000000000000000000000000
χ6644-4-4-4-44-244-4-22200002-22-200002-20000−4i4i00002i−2i2i−2i000000000000000000000000000000
χ678-88i−8i0008000-88i−8i0000000000000000000000000000000000000000000000000000000000
χ688-88i−8i000-40004−4i4i00000000−2ζ2−2ζ7+2ζ10+2ζ112ζ2+2ζ7−2ζ10−2ζ11−2ζ2+2ζ7+2ζ10−2ζ112ζ2−2ζ7−2ζ10+2ζ110000000000000000000000000000000000000000000000
χ698-88i−8i000-40004−4i4i000000002ζ2+2ζ7−2ζ10−2ζ11−2ζ2−2ζ7+2ζ10+2ζ112ζ2−2ζ7−2ζ10+2ζ11−2ζ2+2ζ7+2ζ10−2ζ110000000000000000000000000000000000000000000000
χ708-8−8i8i0008000-8−8i8i0000000000000000000000000000000000000000000000000000000000
χ718-8−8i8i000-400044i−4i00000000−2ζ2+2ζ7+2ζ10−2ζ112ζ2−2ζ7−2ζ10+2ζ11−2ζ2−2ζ7+2ζ10+2ζ112ζ2+2ζ7−2ζ10−2ζ110000000000000000000000000000000000000000000000
χ728-8−8i8i000-400044i−4i000000002ζ2−2ζ7−2ζ10+2ζ11−2ζ2+2ζ7+2ζ10−2ζ112ζ2+2ζ7−2ζ10−2ζ11−2ζ2−2ζ7+2ζ10+2ζ110000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.