Finite Group Databasebeta

← Group #10840281

Character table — Group #10840281

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222222222444444888888888888881212121212121212161616161616161616161616161624242424242424244848
order12442223444612126661212122444888888242424244444888846812121212122424242424242244444448
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111111111111111-11-1111-1-1-1-1-1-1-1-11-11-1-1-111-1-1
χ4111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-1-1-1-11-1111-1-111
χ51111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-11-1-11111-1-1-1-1-11-11-1-111-11
χ61111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-11111-1-1-1-11-11-111-1-11-1
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111111-1
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-1-1-111111111-1-1-1-1-11
χ911111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-111-1-111-1-1111111-1-1-1-11-1
χ1011111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-111-1-111-1-111-1-1-1-11111-11
χ1111111111111111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-11111-1-111-1-11-11-111-1-1-11
χ1211111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-111-1-1-11-11-1-1111-1
χ1311111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-11-1111-1-1-1-1
χ1411111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-11-1-1-11111
χ1511111111111111111111-1-1-1-1-1-1-1-1111111111111111-11-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-11111111111-1-1
χ172222222-1222-1-1-1-1-1-1-1-1-12222222222-1-1-1-1000000002-12-1-1-1-1-1-1-1-1-1-1-10000000000
χ182222222-1222-1-1-1-1-1-1-1-1-12222-2-2-2-222-1-1-1-100000000-2-1-2-1-1-1111111110000000000
χ192222222-1222-1-1-1-1-1-1-1-1-122-2-222-2-2-2-21111000000002-1-2-111-1-1-1-111110000000000
χ202222222-1222-1-1-1-1-1-1-1-1-122-2-2-2-222-2-2111100000000-2-12-1111111-1-1-1-10000000000
χ212222222-1222-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-2111100000000-2121-1-111-1-111-1-10000000000
χ222222222-1222-1-1-1-1-1-1-1-1-1-2-222-2-222-2-211110000000021-21-1-1-1-111-1-1110000000000
χ232222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-100000000-21-211111-1-1-1-1110000000000
χ242222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-100000000212111-1-11111-1-10000000000
χ2522222-2-22-22-22222-2-2-22-2002i−2i0000000000000022-2-200002i−2i000000000000002i−2i00
χ2622222-2-22-22-22222-2-2-22-2002i−2i00000000000000-2-22200002i−2i00000000000000−2i2i00
χ2722222-2-22-22-22222-2-2-22-200−2i2i0000000000000022-2-20000−2i2i00000000000000−2i2i00
χ2822222-2-22-22-22222-2-2-22-200−2i2i00000000000000-2-2220000−2i2i000000000000002i−2i00
χ292222-2-2222-2-2222-22-22-2-20000002i−2i00000022-2-2000000000000002i−2i0000002i−2i0000
χ302222-2-2222-2-2222-22-22-2-20000002i−2i000000-2-222000000000000002i−2i000000−2i2i0000
χ312222-2-2222-2-2222-22-22-2-2000000−2i2i00000022-2-200000000000000−2i2i000000−2i2i0000
χ322222-2-2222-2-2222-22-22-2-2000000−2i2i000000-2-22200000000000000−2i2i0000002i−2i0000
χ3322-2-22-2-222-222-2-22-2-22-2200002i−2i000000002i−2i2i−2i0000000000002i−2i0000020-2000000
χ3422-2-22-2-222-222-2-22-2-22-2200002i−2i00000000−2i2i−2i2i0000000000002i−2i00000-202000000
χ3522-2-22-2-222-222-2-22-2-22-220000−2i2i000000002i−2i2i−2i000000000000−2i2i00000-202000000
χ3622-2-22-2-222-222-2-22-2-22-220000−2i2i00000000−2i2i−2i2i000000000000−2i2i0000020-2000000
χ3722-2-2-22-2222-22-2-2-2-2222-2000000002i−2i2i2i−2i−2i2i−2i−2i2i2-22-2000000000000000000000000
χ3822-2-2-22-2222-22-2-2-2-2222-2000000002i−2i2i2i−2i−2i−2i2i2i−2i-22-22000000000000000000000000
χ3922-2-2-22-2222-22-2-2-2-2222-200000000−2i2i−2i−2i2i2i2i−2i−2i2i-22-22000000000000000000000000
χ4022-2-2-22-2222-22-2-2-2-2222-200000000−2i2i−2i−2i2i2i−2i2i2i−2i2-22-2000000000000000000000000
χ4122-2-2-2-222-2222-2-2-22-2-2222-200000000000000002-2-22020-2000000000020-20000000
χ4222-2-2-2-222-2222-2-2-22-2-2222-20000000000000000-222-2020-20000000000-2020000000
χ4322-2-2-2-222-2222-2-2-22-2-222-2200000000000000002-2-220-2020000000000-2020000000
χ4422-2-2-2-222-2222-2-2-22-2-222-220000000000000000-222-20-202000000000020-20000000
χ4544444-4-4-2-44-4-2-2-2-2222-22004i−4i0000000000000000000000−2i2i000000000000000000
χ4644444-4-4-2-44-4-2-2-2-2222-2200−4i4i00000000000000000000002i−2i000000000000000000
χ474444-44-44-4-44444-4-44-4-440000000000000000000000000000000000000000000000
χ484444-44-4-2-4-44-2-2-222-222-20000000000000000000000000000−2i32i30000000000000000
χ494444-44-4-2-4-44-2-2-222-222-200000000000000000000000000002i3−2i30000000000000000
χ504444-4-44-24-4-4-2-2-22-22-2220000004i−4i000000000000000000000000−2i2i000000000000
χ514444-4-44-24-4-4-2-2-22-22-222000000−4i4i0000000000000000000000002i−2i000000000000
χ5244-4-44444-4-4-44-4-4444-4-4-40000000000000000000000000000000000000000000000
χ5344-4-4444-2-4-4-4-222-2-2-2222000000000000000000000000000000000023−230000000000
χ5444-4-4444-2-4-4-4-222-2-2-22220000000000000000000000000000000000−23230000000000
χ5544-4-44-4-4-24-44-222-222-22-200004i−4i000000000000000000000000−2i2i00000000000000
χ5644-4-44-4-4-24-44-222-222-22-20000−4i4i0000000000000000000000002i−2i00000000000000
χ5744-4-4-44-4-244-4-22222-2-2-22000000004i−4i−2i−2i2i2i00000000000000000000000000000000
χ5844-4-4-44-4-244-4-22222-2-2-2200000000−4i4i2i2i−2i−2i00000000000000000000000000000000
χ5944-4-4-4-44-2-444-2222-222-2-24-4000000000000000000000-20200000000000000000000
χ6044-4-4-4-44-2-444-2222-222-2-2-4400000000000000000000020-200000000000000000000
χ618-88i−8i0008000-88i−8i0000000000000000000000000000000000000000000000000000
χ628-88i−8i000-40004−4i4i00000000000000002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ2300000000000000000000000000000000
χ638-88i−8i000-40004−4i4i0000000000000000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ2300000000000000000000000000000000
χ648-8−8i8i0008000-8−8i8i0000000000000000000000000000000000000000000000000000
χ658-8−8i8i000-400044i−4i0000000000000000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ1300000000000000000000000000000000
χ668-8−8i8i000-400044i−4i00000000000000002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ1300000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.