Finite Group Databasebeta

← Group #10883541

Character table — Group #10883541

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222224444444444444466668888888888888888888888121212121212161616161616161624242424242424244848
order124422234446121266688888888121212888822446688121224242424242424242424242422448846812121224242444888848
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-11-1-1-1-1-1-1-11111-1-1-1-11111111111-11-11-1-1-1-1-1-111-1-111-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-11-11-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11-11-1-1-1-111-1-111-1-111
χ5111111111111111111111-1-1-1-11111111-11-1111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ6111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-11-11111-1-111-1-1-1-111
χ7111111111111111111111-1-1-1-1111-1-1-1-1-11-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-11-1111111-1-11111-1-1
χ911111111111111111-1-1-1-111111111111-11-1111-1-111-1-1-1-1-1-1-1-111111111111-1-1-111-1-111-1-1-1-1-1-11-1
χ1011111111111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111111111-1-11-1-1-111-1-1-1-111-1-1-11
χ1111111111111111111-1-1-1-11111111-1-1-1-1-11-1111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-1-111-1-1-1-1111111-11
χ1211111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1111111-1-1111-1
χ1311111111111111111-1-1-1-1-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-11111-1-1-1-111-11
χ1411111111111111111-1-1-1-1-1-1-1-111111111-11-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-1-1-1-111111-1
χ1511111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1111-1-111-1-11111-1-11-1
χ1611111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-11-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1111-1-11111-1-1-1-1-11
χ172222222-1222-1-1-1-1-1-122222222-1-1-100002222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-12-1-1-1-1-10000000000
χ182222222-1222-1-1-1-1-1-122222222-1-1-100002-22-211-2-211-1-1-1-11111-1-1-1-1000000-2-1-2-111110000000000
χ192222222-1222-1-1-1-1-1-12222-2-2-2-2-1-1-10000-22-22-1-122-1-1-1-1-1-1-1-1-1-11111000000-21-2111110000000000
χ202222222-1222-1-1-1-1-1-12222-2-2-2-2-1-1-10000-2-2-2-211-2-211-1-1-1-1111111110000002121-1-1-1-10000000000
χ212222222-1222-1-1-1-1-1-1-2-2-2-22222-1-1-10000-22-22-1-1-2-2-1-111111111-1-1-1-100000021-21-1-1110000000000
χ222222222-1222-1-1-1-1-1-1-2-2-2-22222-1-1-10000-2-2-2-21122111111-1-1-1-1-1-1-1-1000000-212111-1-10000000000
χ232222222-1222-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-100002222-1-1-2-2-1-1111111111111000000-2-12-111-1-10000000000
χ242222222-1222-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-100002-22-21122111111-1-1-1-111110000002-1-2-1-1-1110000000000
χ252222-22-22-2-222222-2-222-2-20000-22-22222000000000022-2-2000000000000-2-200000000002-2000000
χ262222-22-22-2-222222-2-222-2-20000-22-2-2-2-2-2000000000022-2-2000000000000220000000000-22000000
χ272222-22-22-2-222222-2-2-2-2220000-22-222220000000000-2-222000000000000-2-20000000000-22000000
χ282222-22-22-2-222222-2-2-2-2220000-22-2-2-2-2-20000000000-2-2220000000000002200000000002-2000000
χ2922-2-22222-2-2-22-2-22222i−2i2i−2i0000-2-2-2000000000000002i−2i2i−2i0000000022-2-200000000000000002i−2i00
χ3022-2-22222-2-2-22-2-22222i−2i2i−2i0000-2-2-2000000000000002i−2i2i−2i00000000-2-2220000000000000000−2i2i00
χ3122-2-22222-2-2-22-2-2222−2i2i−2i2i0000-2-2-200000000000000−2i2i−2i2i0000000022-2-20000000000000000−2i2i00
χ3222-2-22222-2-2-22-2-2222−2i2i−2i2i0000-2-2-200000000000000−2i2i−2i2i00000000-2-22200000000000000002i−2i00
χ3322-2-22-2-222-222-2-2-22-20000000022-222-2-20000002i−2i0000002i2i−2i−2i000000002-20000000000002i−2i0000
χ3422-2-22-2-222-222-2-2-22-20000000022-222-2-2000000−2i2i000000−2i−2i2i2i000000002-2000000000000−2i2i0000
χ3522-2-22-2-222-222-2-2-22-20000000022-2-2-2220000002i−2i0000002i2i−2i−2i00000000-22000000000000−2i2i0000
χ3622-2-22-2-222-222-2-2-22-20000000022-2-2-222000000−2i2i000000−2i−2i2i2i00000000-220000000000002i−2i0000
χ3722-2-2-22-2222-22-2-22-2-22i−2i−2i2i2i2i−2i−2i2-22000020-200000002i−2i−2i2i00002i2i−2i−2i000000020-200000000000000
χ3822-2-2-22-2222-22-2-22-2-22i−2i−2i2i−2i−2i2i2i2-220000-20200000002i−2i−2i2i0000−2i−2i2i2i0000000-20200000000000000
χ3922-2-2-22-2222-22-2-22-2-2−2i2i2i−2i2i2i−2i−2i2-220000-2020000000−2i2i2i−2i00002i2i−2i−2i0000000-20200000000000000
χ4022-2-2-22-2222-22-2-22-2-2−2i2i2i−2i−2i−2i2i2i2-22000020-20000000−2i2i2i−2i0000−2i−2i2i2i000000020-200000000000000
χ4122-2-2-22-2-122-2-111-1112i−2i−2i2i2i2i−2i−2i-11-1000020-20−i3i300−i3i3−iii−i3−33−3−i−iii0000000-1013−3−i3i30000000000
χ4222-2-2-22-2-122-2-111-1112i−2i−2i2i2i2i−2i−2i-11-1000020-20i3−i300i3−i3−iii−i−33−33−i−iii0000000-101−33i3−i30000000000
χ4322-2-2-22-2-122-2-111-1112i−2i−2i2i−2i−2i2i2i-11-10000-2020−i3i300−i3i3−iii−i3−33−3ii−i−i000000010-1−33i3−i30000000000
χ4422-2-2-22-2-122-2-111-1112i−2i−2i2i−2i−2i2i2i-11-10000-2020i3−i300i3−i3−iii−i−33−33ii−i−i000000010-13−3−i3i30000000000
χ4522-2-2-22-2-122-2-111-111−2i2i2i−2i2i2i−2i−2i-11-10000-2020−i3i300−i3i3i−i−ii−33−33−i−iii000000010-13−3i3−i30000000000
χ4622-2-2-22-2-122-2-111-111−2i2i2i−2i2i2i−2i−2i-11-10000-2020i3−i300i3−i3i−i−ii3−33−3−i−iii000000010-1−33−i3i30000000000
χ4722-2-2-22-2-122-2-111-111−2i2i2i−2i−2i−2i2i2i-11-1000020-20−i3i300−i3i3i−i−ii−33−33ii−i−i0000000-101−33−i3i30000000000
χ4822-2-2-22-2-122-2-111-111−2i2i2i−2i−2i−2i2i2i-11-1000020-20i3−i300i3−i3i−i−ii3−33−3ii−i−i0000000-1013−3i3−i30000000000
χ4922-2-2-2-222-2222-2-2-2-2200000000-22222-2-2020-22200-2-20000000000000000-22000000002-200000000
χ5022-2-2-2-222-2222-2-2-2-2200000000-22222-2-20-202-2-200220000000000000000-2200000000-2200000000
χ5122-2-2-2-222-2222-2-2-2-2200000000-222-2-222020-22200-2-200000000000000002-200000000-2200000000
χ5222-2-2-2-222-2222-2-2-2-2200000000-222-2-2220-202-2-2002200000000000000002-2000000002-200000000
χ5344444-4-44-44-4444-44-400000000-4-4400000000000000000000000000000000000000000000000000
χ5444444-4-4-2-44-4-2-2-22-220000000022-200000000−2i32i3002i3−2i3000000000000000000000000000000000000
χ5544444-4-4-2-44-4-2-2-22-220000000022-2000000002i3−2i300−2i32i3000000000000000000000000000000000000
χ564444-44-4-2-4-44-2-2-2-22244-4-400002-2200000000000000-2-22200000000000000000000000000000000
χ574444-44-4-2-4-44-2-2-2-222-4-44400002-220000000000000022-2-200000000000000000000000000000000
χ584444-4-4444-4-4444-4-44000000004-4-400000000000000000000000000000000000000000000000000
χ594444-4-44-24-4-4-2-2-222-200000000-222000000000000000000−2i32i32i3−2i30000000000000000000000000000
χ604444-4-44-24-4-4-2-2-222-200000000-2220000000000000000002i3−2i3−2i32i30000000000000000000000000000
χ6144-4-4444-2-4-4-4-222-2-2-24i−4i4i−4i000022200000000000000−2i2i−2i2i00000000000000000000000000000000
χ6244-4-4444-2-4-4-4-222-2-2-2−4i4i−4i4i0000222000000000000002i−2i2i−2i00000000000000000000000000000000
χ6344-4-44-4-4-24-44-2222-2200000000-2-2200000000004i−4i000000−2i−2i2i2i0000000000000000000000000000
χ6444-4-44-4-4-24-44-2222-2200000000-2-220000000000−4i4i0000002i2i−2i−2i0000000000000000000000000000
χ6544-4-4-4-44-2-444-22222-2000000002-2-20000040-4-2-20022000000000000000000000000000000000000
χ6644-4-4-4-44-2-444-22222-2000000002-2-200000-4042200-2-2000000000000000000000000000000000000
χ674-44i−4i0004000-44i−4i00000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300022−22−2i22i20000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-22i−2i00000000000000000000
χ684-44i−4i0004000-44i−4i00000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000−22222i2−2i20000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-22−2i2i00000000000000000000
χ694-44i−4i0004000-44i−4i0000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300022−22−2i22i2000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-22−2i2i00000000000000000000
χ704-44i−4i0004000-44i−4i0000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000−22222i2−2i2000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-22i−2i00000000000000000000
χ714-4−4i4i0004000-4−4i4i0000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300022−222i2−2i2000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-2−2i2i00000000000000000000
χ724-4−4i4i0004000-4−4i4i0000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000−2222−2i22i2000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23-222i−2i00000000000000000000
χ734-4−4i4i0004000-4−4i4i00000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300022−222i2−2i20000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23-222i−2i00000000000000000000
χ744-4−4i4i0004000-4−4i4i00000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000−2222−2i22i20000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232-2−2i2i00000000000000000000
χ758-88i−8i000-40004−4i4i00000004ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ130000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ768-88i−8i000-40004−4i4i0000000−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ1300000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ778-8−8i8i000-400044i−4i0000000−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ2300000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ788-8−8i8i000-400044i−4i00000004ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ230000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000

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