Finite Group Databasebeta

← Group #10897660

Character table — Group #10897660

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222222444444444444888888888888888888121212121212121212121212161616161616161616162424242424244848
order124422234444444612124466612121212121212224444668812121212121212128888888888884681212122424242424888848
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-11-11111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ41111111111111111111111111111111-11-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111111111111111-11-11-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-11-11-1-111-1-1-1-1-1-1-1-111
χ6111111111111111111111111111111-11-11-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-111-1-1111111-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111-11-111-1-1111111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-111-1-1-1-11111
χ911111111-1-1-1-1111111-1-111111-1-1-1-111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-111-11
χ1011111111-1-1-1-1111111-1-111111-1-1-1-111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-111-1-111-1-11-1
χ1111111111-1-1-1-1111111-1-111111-1-1-1-111-11-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-111111-1
χ1211111111-1-1-1-1111111-1-111111-1-1-1-111-11-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1-111-1-1-1-1-11
χ1311111111-1-1-1-1111111-1-111111-1-1-1-11-11-1111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1111-1-1-1-1-1-111-1-1-11
χ1411111111-1-1-1-1111111-1-111111-1-1-1-11-11-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1111-1-1-1-111-1-1111-1
χ1511111111-1-1-1-1111111-1-111111-1-1-1-11-1-1-1-111-1-111-1-1-1-1111111111111-1-1-1-1-1-11-1-1-1111111-1-1-1-11-1
χ1611111111-1-1-1-1111111-1-111111-1-1-1-11-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-1-1-11111-1-11111-11
χ172222222-12222222-1-1-122-1-1-1-1-1-1-1-1-1-1222222-1-122-1-1-1-1-1-1-1-10000000000002-12-1-1-1-1-1-1-100000000
χ182222222-12222222-1-1-122-1-1-1-1-1-1-1-1-1-12-22-222-1-1-2-2-1-1-1-1-1-1-1-1000000000000-21-2111111100000000
χ192222222-12222222-1-1-122-1-1-1-1-1-1-1-1-1-1-22-22-2-2112211-1-11111000000000000-2-1-2-111-1-11100000000
χ202222222-12222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211-2-211-1-111110000000000002121-1-111-1-100000000
χ212222222-1-2-2-2-2222-1-1-1-2-2-1-1-1-1-11111-12222-2-2-1-1-2-2-1-1111111000000000000-2-12-11111-1-100000000
χ222222222-1-2-2-2-2222-1-1-1-2-2-1-1-1-1-11111-12-22-2-2-2-1-122-1-111111100000000000021-21-1-1-1-11100000000
χ232222222-1-2-2-2-2222-1-1-1-2-2-1-1-1-1-11111-1-22-222211-2-21111-1-1-1-10000000000002-1-2-1-1-1111100000000
χ242222222-1-2-2-2-2222-1-1-1-2-2-1-1-1-1-11111-1-2-2-2-22211221111-1-1-1-1000000000000-212111-1-1-1-100000000
χ252222-22-222222-2-22222-2-2-2-222-22222-2000000000000-2-20000000022-2-20000000000000000002-200
χ262222-22-222222-2-22222-2-2-2-222-22222-2000000000000-2-200000000-2-222000000000000000000-2200
χ272222-22-22-2-2-2-2-2-2222222-2-222-2-2-2-2-2-2000000000000220000000022-2-2000000000000000000-2200
χ282222-22-22-2-2-2-2-2-2222222-2-222-2-2-2-2-2-20000000000002200000000-2-2220000000000000000002-200
χ2922-2-222220000-2-2-22-2-200222-2-20000-200002-20000000022-2-22i2i−2i−2i2i−2i2i−2i0000000000000000000000
χ3022-2-222220000-2-2-22-2-200222-2-20000-200002-20000000022-2-2−2i−2i2i2i−2i2i−2i2i0000000000000000000000
χ3122-2-222220000-2-2-22-2-200222-2-20000-20000-2200000000-2-2222i2i−2i−2i−2i2i−2i2i0000000000000000000000
χ3222-2-222220000-2-2-22-2-200222-2-20000-20000-2200000000-2-222−2i−2i2i2i2i−2i2i−2i0000000000000000000000
χ3322-2-22-2-222i2i−2i−2i-2222-2-22i−2i-22-2222i2i−2i−2i-20000000000002i−2i000000000000000000000000002-22i−2i0000
χ3422-2-22-2-222i2i−2i−2i-2222-2-22i−2i-22-2222i2i−2i−2i-20000000000002i−2i00000000000000000000000000-22−2i2i0000
χ3522-2-22-2-22−2i−2i2i2i-2222-2-2−2i2i-22-222−2i−2i2i2i-2000000000000−2i2i000000000000000000000000002-2−2i2i0000
χ3622-2-22-2-22−2i−2i2i2i-2222-2-2−2i2i-22-222−2i−2i2i2i-2000000000000−2i2i00000000000000000000000000-222i−2i0000
χ3722-2-2-22-22000022-22-2-200-2-22-220000220-20002200-2-200000000002i−2i−2i2i2i2i−2i−2i000000000000000000
χ3822-2-2-22-22000022-22-2-200-2-22-220000220-20002200-2-20000000000−2i2i2i−2i−2i−2i2i2i000000000000000000
χ3922-2-2-22-22000022-22-2-200-2-22-2200002-202000-2-2002200000000002i−2i−2i2i−2i−2i2i2i000000000000000000
χ4022-2-2-22-22000022-22-2-200-2-22-2200002-202000-2-200220000000000−2i2i2i−2i2i2i−2i−2i000000000000000000
χ4122-2-2-2-2222i2i−2i−2i2-222-2-2−2i2i2-2-22-22i2i−2i−2i2020-200002i−2i00−2i2i0000000000000000020-2002i−2i0000000000
χ4222-2-2-2-2222i2i−2i−2i2-222-2-2−2i2i2-2-22-22i2i−2i−2i20-2020000−2i2i00−2i2i00000000000000000-20200−2i2i0000000000
χ4322-2-2-2-222−2i−2i2i2i2-222-2-22i−2i2-2-22-2−2i−2i2i2i2020-20000−2i2i002i−2i0000000000000000020-200−2i2i0000000000
χ4422-2-2-2-222−2i−2i2i2i2-222-2-22i−2i2-2-22-2−2i−2i2i2i20-20200002i−2i002i−2i00000000000000000-202002i−2i0000000000
χ4522-2-2-2-22-12i2i−2i−2i2-22-111−2i2i-111-11−i−iii-1020-200−i3i32i−2i−i3i3i−i3−33−30000000000000-1013−3−ii−i3i300000000
χ4622-2-2-2-22-12i2i−2i−2i2-22-111−2i2i-111-11−i−iii-1020-200i3−i32i−2ii3−i3i−i−33−330000000000000-101−33−iii3−i300000000
χ4722-2-2-2-22-12i2i−2i−2i2-22-111−2i2i-111-11−i−iii-10-20200−i3i3−2i2i−i3i3i−i3−33−3000000000000010-1−33i−ii3−i300000000
χ4822-2-2-2-22-12i2i−2i−2i2-22-111−2i2i-111-11−i−iii-10-20200i3−i3−2i2ii3−i3i−i−33−33000000000000010-13−3i−i−i3i300000000
χ4922-2-2-2-22-1−2i−2i2i2i2-22-1112i−2i-111-11ii−i−i-1020-200−i3i3−2i2i−i3i3−ii−33−330000000000000-101−33i−i−i3i300000000
χ5022-2-2-2-22-1−2i−2i2i2i2-22-1112i−2i-111-11ii−i−i-1020-200i3−i3−2i2ii3−i3−ii3−33−30000000000000-1013−3i−ii3−i300000000
χ5122-2-2-2-22-1−2i−2i2i2i2-22-1112i−2i-111-11ii−i−i-10-20200−i3i32i−2i−i3i3−ii−33−33000000000000010-13−3−iii3−i300000000
χ5222-2-2-2-22-1−2i−2i2i2i2-22-1112i−2i-111-11ii−i−i-10-20200i3−i32i−2ii3−i3−ii3−33−3000000000000010-1−33−ii−i3i300000000
χ5344444-4-4400004-4-444400-44-4-4-400004000000000000000000000000000000000000000000000000
χ5444444-4-4-200004-4-4-2-2-2002-22220000-2000000−2i32i3002i3−2i3000000000000000000000000000000000000
χ5544444-4-4-200004-4-4-2-2-2002-22220000-20000002i3−2i300−2i32i3000000000000000000000000000000000000
χ564444-44-4-24444-4-44-2-2-2-4-422-2-22-2-2-2-22000000000000220000000000000000000000000000000000
χ574444-44-4-2-4-4-4-4-4-44-2-2-24422-2-2222222000000000000-2-20000000000000000000000000000000000
χ584444-4-4440000-44-4444004-4-4-440000-4000000000000000000000000000000000000000000000000
χ594444-4-44-20000-44-4-2-2-200-2222-2000020000000000000023−23−2323000000000000000000000000000000
χ604444-4-44-20000-44-4-2-2-200-2222-20000200000000000000−232323−23000000000000000000000000000000
χ6144-4-4444-20000-4-4-4-22200-2-2-2220000200004-400000000-2-222000000000000000000000000000000
χ6244-4-4444-20000-4-4-4-22200-2-2-222000020000-440000000022-2-2000000000000000000000000000000
χ6344-4-44-4-4-24i4i−4i−4i-444-2224i−4i2-22-2-2−2i−2i2i2i2000000000000−2i2i0000000000000000000000000000000000
χ6444-4-44-4-4-2−4i−4i4i4i-444-222−4i4i2-22-2-22i2i−2i−2i20000000000002i−2i0000000000000000000000000000000000
χ6544-4-4-44-4-2000044-4-2220022-22-20000-240-4000-2-20022000000000000000000000000000000000000
χ6644-4-4-44-4-2000044-4-2220022-22-20000-2-4040002200-2-2000000000000000000000000000000000000
χ674-44i−4i00042+2i−2−2i2−2i−2+2i000-44i−4i00000002+2i−2−2i2−2i−2+2i00000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ684-44i−4i00042+2i−2−2i2−2i−2+2i000-44i−4i00000002+2i−2−2i2−2i−2+2i0000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ694-44i−4i0004−2−2i2+2i−2+2i2−2i000-44i−4i0000000−2−2i2+2i−2+2i2−2i00000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ704-44i−4i0004−2−2i2+2i−2+2i2−2i000-44i−4i0000000−2−2i2+2i−2+2i2−2i0000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ714-4−4i4i00042−2i−2+2i2+2i−2−2i000-4−4i4i00000002−2i−2+2i2+2i−2−2i0000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ724-4−4i4i00042−2i−2+2i2+2i−2−2i000-4−4i4i00000002−2i−2+2i2+2i−2−2i00000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ734-4−4i4i0004−2+2i2−2i−2−2i2+2i000-4−4i4i0000000−2+2i2−2i−2−2i2+2i0000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ744-4−4i4i0004−2+2i2−2i−2−2i2+2i000-4−4i4i0000000−2+2i2−2i−2−2i2+2i00000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ758-88i−8i000-44+4i−4−4i4−4i−4+4i0004−4i4i0000000−2−2i2+2i−2+2i2−2i0000000000000000000000000000000000000000000000000
χ768-88i−8i000-4−4−4i4+4i−4+4i4−4i0004−4i4i00000002+2i−2−2i2−2i−2+2i0000000000000000000000000000000000000000000000000
χ778-8−8i8i000-44−4i−4+4i4+4i−4−4i00044i−4i0000000−2+2i2−2i−2−2i2+2i0000000000000000000000000000000000000000000000000
χ788-8−8i8i000-4−4+4i4−4i−4−4i4+4i00044i−4i00000002−2i−2+2i2+2i−2−2i0000000000000000000000000000000000000000000000000

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