Finite Group Databasebeta

← Group #10840283

Character table — Group #10840283

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order124422234446121244446661212121212121222444466881212121212121212888846812121224242424244444888848
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-11-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ411111111111111111111111111111-11-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ51111111111111111111111111111-11-11-1-1-1-111-1-111-1-1-1-11111-11-11-1-111-1-1-1-111-1-11111-1-1
χ61111111111111111111111111111-11-11-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-11-111-1-111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-11-111-1-11111111111-1-1-1-1
χ911111111111111-1-1-1-111111-1-1-1-111111-1-111-1-111-1-1-1-1-1-11111-1111-1-1-1-11111-1-1-1-111-1-1-11
χ1011111111111111-1-1-1-111111-1-1-1-111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1111-1
χ1111111111111111-1-1-1-111111-1-1-1-111-11-1-1-1111111-1-1-1-1-1-111111-1-1-11111-1-11111-1-1-1-1-1-11-1
χ1211111111111111-1-1-1-111111-1-1-1-111-11-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-1-1111111-11
χ1311111111111111-1-1-1-111111-1-1-1-11-11-1111-1-1-1-1-1-1-1-11111111111-1111-1-1-1-1-1-1-1-11111-1-11-1
χ1411111111111111-1-1-1-111111-1-1-1-11-11-1111-1-1-1-1-1-1-1-11111-1-1-1-111-1111-1-1-1-11111-1-1-1-111-11
χ1511111111111111-1-1-1-111111-1-1-1-11-1-1-1-111-1-111-1-1-1-111111111-1-11-1-1-11111-1-11111-1-1-1-1-11
χ1611111111111111-1-1-1-111111-1-1-1-11-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11-1-1-1111111-1-1-1-111111-1
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
χ2522222-2-22-22-222200002-2-22-20000-200002i−2i000000002i2i−2i−2i22-2-2000000000000002i−2i000000
χ2622222-2-22-22-222200002-2-22-20000-200002i−2i000000002i2i−2i−2i-2-22200000000000000−2i2i000000
χ2722222-2-22-22-222200002-2-22-20000-20000−2i2i00000000−2i−2i2i2i22-2-200000000000000−2i2i000000
χ2822222-2-22-22-222200002-2-22-20000-20000−2i2i00000000−2i−2i2i2i-2-222000000000000002i−2i000000
χ292222-2-2222-2-222222-2-2-2-22-222222-2000000000000-2-2000000000000000000002i−2i002i−2i0000
χ302222-2-2222-2-222222-2-2-2-22-222222-2000000000000-2-200000000000000000000−2i2i00−2i2i0000
χ312222-2-2222-2-2222-2-222-2-22-22-2-2-2-2-200000000000022000000000000000000002i−2i00−2i2i0000
χ322222-2-2222-2-2222-2-222-2-22-22-2-2-2-2-20000000000002200000000000000000000−2i2i002i−2i0000
χ3322-2-22-2-222-222-2-22i−2i2i−2i2-2-2-222i2i−2i−2i2020-200002i−2i002i−2i00000000020-2002i−2i00000000000000
χ3422-2-22-2-222-222-2-22i−2i2i−2i2-2-2-222i2i−2i−2i20-2020000−2i2i002i−2i000000000-20200−2i2i00000000000000
χ3522-2-22-2-222-222-2-2−2i2i−2i2i2-2-2-22−2i−2i2i2i2020-20000−2i2i00−2i2i00000000020-200−2i2i00000000000000
χ3622-2-22-2-222-222-2-2−2i2i−2i2i2-2-2-22−2i−2i2i2i20-20200002i−2i00−2i2i000000000-202002i−2i00000000000000
χ3722-2-22-2-2-12-22-1112i−2i2i−2i-1111-1−i−iii-1020-200−i3i32i−2i−i3i3−ii3−33−300000-1013−3−ii−i3i3000000000000
χ3822-2-22-2-2-12-22-1112i−2i2i−2i-1111-1−i−iii-1020-200i3−i32i−2ii3−i3−ii−33−3300000-101−33−iii3−i3000000000000
χ3922-2-22-2-2-12-22-1112i−2i2i−2i-1111-1−i−iii-10-20200−i3i3−2i2i−i3i3−ii3−33−30000010-1−33i−ii3−i3000000000000
χ4022-2-22-2-2-12-22-1112i−2i2i−2i-1111-1−i−iii-10-20200i3−i3−2i2ii3−i3−ii−33−330000010-13−3i−i−i3i3000000000000
χ4122-2-22-2-2-12-22-111−2i2i−2i2i-1111-1ii−i−i-1020-200−i3i3−2i2i−i3i3i−i−33−3300000-101−33i−i−i3i3000000000000
χ4222-2-22-2-2-12-22-111−2i2i−2i2i-1111-1ii−i−i-1020-200i3−i3−2i2ii3−i3i−i3−33−300000-1013−3i−ii3−i3000000000000
χ4322-2-22-2-2-12-22-111−2i2i−2i2i-1111-1ii−i−i-10-20200−i3i32i−2i−i3i3i−i−33−330000010-13−3−iii3−i3000000000000
χ4422-2-22-2-2-12-22-111−2i2i−2i2i-1111-1ii−i−i-10-20200i3−i32i−2ii3−i3i−i3−33−30000010-1−33−ii−i3i3000000000000
χ4522-2-2-22-2222-22-2-22i−2i−2i2i-22-2222i2i−2i−2i-2000000000000−2i2i00002-22-20000000000000000002i−2i00
χ4622-2-2-22-2222-22-2-22i−2i−2i2i-22-2222i2i−2i−2i-2000000000000−2i2i0000-22-22000000000000000000−2i2i00
χ4722-2-2-22-2222-22-2-2−2i2i2i−2i-22-222−2i−2i2i2i-20000000000002i−2i00002-22-2000000000000000000−2i2i00
χ4822-2-2-22-2222-22-2-2−2i2i2i−2i-22-222−2i−2i2i2i-20000000000002i−2i0000-22-220000000000000000002i−2i00
χ4922-2-2-2-222-2222-2-20000-2-222-20000220-20002200-2-20000002-2-2200000000002-20000000000
χ5022-2-2-2-222-2222-2-20000-2-222-20000220-20002200-2-2000000-222-20000000000-220000000000
χ5122-2-2-2-222-2222-2-20000-2-222-200002-202000-2-200220000002-2-220000000000-220000000000
χ5222-2-2-2-222-2222-2-20000-2-222-200002-202000-2-20022000000-222-200000000002-20000000000
χ5344444-4-4-2-44-4-2-2-20000-222-220000200004i−4i00000000−2i−2i2i2i00000000000000000000000000
χ5444444-4-4-2-44-4-2-2-20000-222-22000020000−4i4i000000002i2i−2i−2i00000000000000000000000000
χ554444-44-44-4-444440000-44-4-4-40000400000000000000000000000000000000000000000000
χ564444-44-4-2-4-44-2-2-200002-22220000-2000000−2i32i3002i3−2i300000000000000000000000000000000
χ574444-44-4-2-4-44-2-2-200002-22220000-20000002i3−2i300−2i32i300000000000000000000000000000000
χ584444-4-44-24-4-4-2-2-244-4-422-22-2-2-2-2-2200000000000022000000000000000000000000000000
χ594444-4-44-24-4-4-2-2-2-4-44422-22-222222000000000000-2-2000000000000000000000000000000
χ6044-4-44444-4-4-44-4-40000444-4-40000-400000000000000000000000000000000000000000000
χ6144-4-4444-2-4-4-4-2220000-2-2-2220000200000000000000−2i32i32i3−2i300000000000000000000000000
χ6244-4-4444-2-4-4-4-2220000-2-2-22200002000000000000002i3−2i3−2i32i300000000000000000000000000
χ6344-4-4-44-4-244-4-2224i−4i−4i4i2-22-2-2−2i−2i2i2i20000000000002i−2i000000000000000000000000000000
χ6444-4-4-44-4-244-4-222−4i4i4i−4i2-22-2-22i2i−2i−2i2000000000000−2i2i000000000000000000000000000000
χ6544-4-4-4-44-2-444-222000022-2-220000-240-4000-2-2002200000000000000000000000000000000
χ6644-4-4-4-44-2-444-222000022-2-220000-2-4040002200-2-200000000000000000000000000000000
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.