Finite Group Databasebeta

← Group #10827747

Character table — Group #10827747

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order124422234446121244446661212121212121222444466881212121212121212224446812121224242424224444448848
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-11-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-1
χ411111111111111111111111111111-11-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111
χ51111111111111111111111111111-11-11-1-1-1-111-1-111-1-1-1-11111-11-11-1-111-1-1-11-1111-1-111-1-1
χ61111111111111111111111111111-11-11-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11-11-1-111-1-11-11-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-11-111-1-111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-11-111-1-1111111-1-11111-1-1
χ911111111111111-1-1-1-111111-1-1-1-111111-1-111-1-111-1-1-1-1-1-11111-1111-1-1-1-111-11-11-1-111-1-1-11
χ1011111111111111-1-1-1-111111-1-1-1-111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-11-111-1-1111-1
χ1111111111111111-1-1-1-111111-1-1-1-111-11-1-1-1111111-1-1-1-1-1-111111-1-1-11111-1-1-1-1-1-1-1-111111-1
χ1211111111111111-1-1-1-111111-1-1-1-111-11-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1111111-1-1-1-1-11
χ1311111111111111-1-1-1-111111-1-1-1-11-11-1111-1-1-1-1-1-1-1-11111111111-1111-1-1-1-11111-1-1-1-1-1-11-1
χ1411111111111111-1-1-1-111111-1-1-1-11-11-1111-1-1-1-1-1-1-1-11111-1-1-1-111-1111-1-1-1-1-1-1-1-1111111-11
χ1511111111111111-1-1-1-111111-1-1-1-11-1-1-1-111-1-111-1-1-1-111111111-1-11-1-1-111111-11-1-1-1-1-111-11
χ1611111111111111-1-1-1-111111-1-1-1-11-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11-1-1-11111-11-111111-1-11-1
χ172222222-1222-1-1-12222-1-1-1-1-1-1-1-1-1-1222222-1-122-1-1-1-1-1-1-1-100002-12-1-1-1-1-1-1-1000000000000
χ182222222-1222-1-1-12222-1-1-1-1-1-1-1-1-1-12-22-222-1-1-2-2-1-1-1-1-1-1-1-10000-21-21111111000000000000
χ192222222-1222-1-1-12222-1-1-1-1-1-1-1-1-1-1-22-22-2-2112211-1-111110000-2-1-2-111-1-111000000000000
χ202222222-1222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211-2-211-1-1111100002121-1-111-1-1000000000000
χ212222222-1222-1-1-1-2-2-2-2-1-1-1-1-11111-12222-2-2-1-1-2-2-1-11111110000-2-12-11111-1-1000000000000
χ222222222-1222-1-1-1-2-2-2-2-1-1-1-1-11111-12-22-2-2-2-1-122-1-1111111000021-21-1-1-1-111000000000000
χ232222222-1222-1-1-1-2-2-2-2-1-1-1-1-11111-1-22-222211-2-21111-1-1-1-100002-1-2-1-1-11111000000000000
χ242222222-1222-1-1-1-2-2-2-2-1-1-1-1-11111-1-2-2-2-22211221111-1-1-1-10000-212111-1-1-1-1000000000000
χ252222-2-2222-2-222222-2-2-2-222-22222-2000000000000-2-200002-22-2000000000000002-2000000
χ262222-2-2222-2-222222-2-2-2-222-22222-2000000000000-2-20000-22-2200000000000000-22000000
χ272222-2-2222-2-2222-2-222-2-222-2-2-2-2-2-20000000000002200002-22-200000000000000-22000000
χ282222-2-2222-2-2222-2-222-2-222-2-2-2-2-2-2000000000000220000-22-22000000000000002-2000000
χ2922-2-22222-2-2-22-2-20000222-2-20000-200002-20000000022-2-22-2-22000000000020-2000000000
χ3022-2-22222-2-2-22-2-20000222-2-20000-200002-20000000022-2-2-222-20000000000-202000000000
χ3122-2-22222-2-2-22-2-20000222-2-20000-20000-2200000000-2-2222-2-220000000000-202000000000
χ3222-2-22222-2-2-22-2-20000222-2-20000-20000-2200000000-2-222-222-2000000000020-2000000000
χ3322-2-22-2-222-222-2-22i−2i2i−2i-22-2222i2i−2i−2i-20000000000002i−2i000000000000000000020-200002i−2i00
χ3422-2-22-2-222-222-2-22i−2i2i−2i-22-2222i2i−2i−2i-20000000000002i−2i0000000000000000000-2020000−2i2i00
χ3522-2-22-2-222-222-2-2−2i2i−2i2i-22-222−2i−2i2i2i-2000000000000−2i2i000000000000000000020-20000−2i2i00
χ3622-2-22-2-222-222-2-2−2i2i−2i2i-22-222−2i−2i2i2i-2000000000000−2i2i0000000000000000000-20200002i−2i00
χ3722-2-2-22-2222-22-2-22i−2i−2i2i2-2-22-22i2i−2i−2i2020-200002i−2i00−2i2i00000000020-2002i−2i00000000000000
χ3822-2-2-22-2222-22-2-22i−2i−2i2i2-2-22-22i2i−2i−2i20-2020000−2i2i00−2i2i000000000-20200−2i2i00000000000000
χ3922-2-2-22-2222-22-2-2−2i2i2i−2i2-2-22-2−2i−2i2i2i2020-20000−2i2i002i−2i00000000020-200−2i2i00000000000000
χ4022-2-2-22-2222-22-2-2−2i2i2i−2i2-2-22-2−2i−2i2i2i20-20200002i−2i002i−2i000000000-202002i−2i00000000000000
χ4122-2-2-22-2-122-2-1112i−2i−2i2i-111-11−i−iii-1020-200−i3i32i−2i−i3i3i−i3−33−300000-1013−3−ii−i3i3000000000000
χ4222-2-2-22-2-122-2-1112i−2i−2i2i-111-11−i−iii-1020-200i3−i32i−2ii3−i3i−i−33−3300000-101−33−iii3−i3000000000000
χ4322-2-2-22-2-122-2-1112i−2i−2i2i-111-11−i−iii-10-20200−i3i3−2i2i−i3i3i−i3−33−30000010-1−33i−ii3−i3000000000000
χ4422-2-2-22-2-122-2-1112i−2i−2i2i-111-11−i−iii-10-20200i3−i3−2i2ii3−i3i−i−33−330000010-13−3i−i−i3i3000000000000
χ4522-2-2-22-2-122-2-111−2i2i2i−2i-111-11ii−i−i-1020-200−i3i3−2i2i−i3i3−ii−33−3300000-101−33i−i−i3i3000000000000
χ4622-2-2-22-2-122-2-111−2i2i2i−2i-111-11ii−i−i-1020-200i3−i3−2i2ii3−i3−ii3−33−300000-1013−3i−ii3−i3000000000000
χ4722-2-2-22-2-122-2-111−2i2i2i−2i-111-11ii−i−i-10-20200−i3i32i−2i−i3i3−ii−33−330000010-13−3−iii3−i3000000000000
χ4822-2-2-22-2-122-2-111−2i2i2i−2i-111-11ii−i−i-10-20200i3−i32i−2ii3−i3−ii3−33−30000010-1−33−ii−i3i3000000000000
χ4922-2-2-2-222-2222-2-20000-2-22-220000220-20002200-2-200000022-2-200000000000000002-20000
χ5022-2-2-2-222-2222-2-20000-2-22-220000220-20002200-2-2000000-2-2220000000000000000-220000
χ5122-2-2-2-222-2222-2-20000-2-22-2200002-202000-2-2002200000022-2-20000000000000000-220000
χ5222-2-2-2-222-2222-2-20000-2-22-2200002-202000-2-20022000000-2-22200000000000000002-20000
χ5344444-4-44-44-44440000-44-4-4-40000400000000000000000000000000000000000000000000
χ5444444-4-4-2-44-4-2-2-200002-22220000-2000000−2i32i3002i3−2i300000000000000000000000000000000
χ5544444-4-4-2-44-4-2-2-200002-22220000-20000002i3−2i300−2i32i300000000000000000000000000000000
χ564444-44-44-4-4444400004-4-4-440000-400000000000000000000000000000000000000000000
χ574444-44-4-2-4-44-2-2-20000-2222-2000020000000000000023−23−232300000000000000000000000000
χ584444-44-4-2-4-44-2-2-20000-2222-20000200000000000000−232323−2300000000000000000000000000
χ594444-4-44-24-4-4-2-2-244-4-422-2-22-2-2-2-2200000000000022000000000000000000000000000000
χ604444-4-44-24-4-4-2-2-2-4-44422-2-2222222000000000000-2-2000000000000000000000000000000
χ6144-4-4444-2-4-4-4-2220000-2-2-2220000200004-400000000-2-22200000000000000000000000000
χ6244-4-4444-2-4-4-4-2220000-2-2-222000020000-440000000022-2-200000000000000000000000000
χ6344-4-44-4-4-24-44-2224i−4i4i−4i2-22-2-2−2i−2i2i2i2000000000000−2i2i000000000000000000000000000000
χ6444-4-44-4-4-24-44-222−4i4i−4i4i2-22-2-22i2i−2i−2i20000000000002i−2i000000000000000000000000000000
χ6544-4-4-4-44-2-444-222000022-22-20000-240-4000-2-2002200000000000000000000000000000000
χ6644-4-4-4-44-2-444-222000022-22-20000-2-4040002200-2-200000000000000000000000000000000
χ678-88i−8i0008000-88i−8i0000000000000000000000000000000000000000000000000000000000
χ688-88i−8i000-40004−4i4i000000000−2ζ2−2ζ7+2ζ10+2ζ112ζ2+2ζ7−2ζ10−2ζ11−2ζ2+2ζ7+2ζ10−2ζ112ζ2−2ζ7−2ζ10+2ζ11000000000000000000000000000000000000000000000
χ698-88i−8i000-40004−4i4i0000000002ζ2+2ζ7−2ζ10−2ζ11−2ζ2−2ζ7+2ζ10+2ζ112ζ2−2ζ7−2ζ10+2ζ11−2ζ2+2ζ7+2ζ10−2ζ11000000000000000000000000000000000000000000000
χ708-8−8i8i0008000-8−8i8i0000000000000000000000000000000000000000000000000000000000
χ718-8−8i8i000-400044i−4i000000000−2ζ2+2ζ7+2ζ10−2ζ112ζ2−2ζ7−2ζ10+2ζ11−2ζ2−2ζ7+2ζ10+2ζ112ζ2+2ζ7−2ζ10−2ζ11000000000000000000000000000000000000000000000
χ728-8−8i8i000-400044i−4i0000000002ζ2−2ζ7−2ζ10+2ζ11−2ζ2+2ζ7+2ζ10−2ζ112ζ2+2ζ7−2ζ10−2ζ11−2ζ2−2ζ7+2ζ10+2ζ11000000000000000000000000000000000000000000000

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