Finite Group Databasebeta

← Group #11778217

Character table — Group #11778217

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444448888888888888888888888888121224242424242424242424242424242424242424484872727272
order122222336666666666344666666666121244121212121212121212121212121212121212121212121222244446688121212121212242424246122488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-11-11111-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-11-11-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-11-1-1-1111111-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-11111-1-1-1-111-1-111
χ811111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-111-1-1
χ92222222222222222222-2-2222222222-2-200-2-2-200000000-2-2-2-200000000220-20002200-2-200000000000000
χ102222222222222222222-2-2222222222-2-200-2-2-200000000-2-2-2-200000000-2-202000-2-2002200000000000000
χ112222222-1222-12222-1-1-122-1-1-1-1-1-1-1-1-1-1-12222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100202000022000000-1-1-1-1-1-10000
χ122222222-1222-12222-1-1-122-1-1-1-1-1-1-1-1-1-1-12222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-20-20000-2-20000001111110000
χ132222222-1222-12222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-2-222-1-2-2-2-21111-1-1-1-111111111002020000-2-20000001111-1-10000
χ142222222-1222-12222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-2-222-1-2-2-2-21111-1-1-1-11111111100-20-2000022000000-1-1-1-1110000
χ15222222-12-1-1-12-1-1-1-122-12222-1-1-1-1-1-1-12222-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12202022-1-100-1-1-1-1-1-10000000000
χ16222222-12-1-1-12-1-1-1-122-12222-1-1-1-1-1-1-12222-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-20-20-2-211001111110000000000
χ17222222-12-1-1-12-1-1-1-122-12222-1-1-1-1-1-1-122-2-2-1-121111-2-2-2-2-1-1-1-11111111122020-2-2-1-100-1-111110000000000
χ18222222-12-1-1-12-1-1-1-122-12222-1-1-1-1-1-1-122-2-2-1-121111-2-2-2-2-1-1-1-111111111-2-20-2022110011-1-1-1-10000000000
χ19222222-12-1-1-12-1-1-1-122-1-2-222-1-1-1-1-1-1-1-2-20011-2−i3−i3i3i300001111−i3−i3−i3−i3i3i3i3i3220-2000-1-10011−i3−i3i3i30000000000
χ20222222-12-1-1-12-1-1-1-122-1-2-222-1-1-1-1-1-1-1-2-20011-2−i3−i3i3i300001111−i3−i3−i3−i3i3i3i3i3-2-2020001100-1-1i3i3−i3−i30000000000
χ21222222-12-1-1-12-1-1-1-122-1-2-222-1-1-1-1-1-1-1-2-20011-2i3i3−i3−i300001111i3i3i3i3−i3−i3−i3−i3220-2000-1-10011i3i3−i3−i30000000000
χ22222222-12-1-1-12-1-1-1-122-1-2-222-1-1-1-1-1-1-1-2-20011-2i3i3−i3−i300001111i3i3i3i3−i3−i3−i3−i3-2-2020001100-1-1−i3−i3i3i30000000000
χ232222-2-2222-2-2222-2-22222-2-2-222-2-2-2-2222002-2-20000000022-2-2000000000020-200000000000000002-20000
χ242222-2-2222-2-2222-2-22222-2-2-222-2-2-2-2222002-2-20000000022-2-20000000000-2020000000000000000-220000
χ252222-2-2222-2-2222-2-2222-22-2-222-2-2-2-22-2-200-22200000000-2-22200000000000000000000000000000002-200
χ262222-2-2222-2-2222-2-2222-22-2-222-2-2-2-22-2-200-22200000000-2-2220000000000000000000000000000000-2200
χ272222-2-22-12-2-2-122-2-2-1-1-12-211-1-11111-1-1-1002-210000−i3−i3i3i3-1-111−i3−i3i3i3−i3−i3i3i30020-2000000000000−i3−i3i3i3-110000
χ282222-2-22-12-2-2-122-2-2-1-1-12-211-1-11111-1-1-1002-210000−i3−i3i3i3-1-111−i3−i3i3i3−i3−i3i3i300-202000000000000i3i3−i3−i31-10000
χ292222-2-22-12-2-2-122-2-2-1-1-12-211-1-11111-1-1-1002-210000i3i3−i3−i3-1-111i3i3−i3−i3i3i3−i3−i30020-2000000000000i3i3−i3−i3-110000
χ302222-2-22-12-2-2-122-2-2-1-1-12-211-1-11111-1-1-1002-210000i3i3−i3−i3-1-111i3i3−i3−i3i3i3−i3−i300-202000000000000−i3−i3i3i31-10000
χ312-2-222-222222-2-2-2-2-22-22002-22-222-2-2-20000000000000000000000000002-2000002-2−i2i2000000−i2i2−i2i20000−i2i2
χ322-2-222-222222-2-2-2-2-22-22002-22-222-2-2-20000000000000000000000000002-2000002-2i2−i2000000i2−i2i2−i20000i2−i2
χ332-2-222-222222-2-2-2-2-22-22002-22-222-2-2-2000000000000000000000000000-2200000-22−i2i2000000−i2i2−i2i20000i2−i2
χ342-2-222-222222-2-2-2-2-22-22002-22-222-2-2-2000000000000000000000000000-2200000-22i2−i2000000i2−i2i2−i20000−i2i2
χ354444444-2444-24444-2-2-2-4-4-2-2-2-2-2-2-2-2-22200-4-4200000000222200000000000000000000000000000000000
χ36444444-2-2-2-2-2-2-2-2-2-2-2-2144-2-21111111-2-244-2-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000
χ37444444-2-2-2-2-2-2-2-2-2-2-2-2144-2-21111111-2-2-4-4-2-2-2222222221111-1-1-1-1-1-1-1-1000000000000000000000000000
χ38444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-2-211111112200222−2i3−2i32i32i30000-1-1-1-1i3i3i3i3−i3−i3−i3−i3000000000000000000000000000
χ39444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-2-2111111122002222i32i3−2i3−2i30000-1-1-1-1−i3−i3−i3−i3i3i3i3i3000000000000000000000000000
χ404444-4-44-24-4-4-244-4-4-2-2-2-4422-2-22222-22200-44-20000000022-2-200000000000000000000000000000000000
χ414444-4-4-24-2224-2-22244-24-4-4-4-2-22222-24400-22-400000000-2-22200000000000000000000000000000000000
χ424444-4-4-24-2224-2-22244-2-44-4-4-2-22222-2-4-4002-240000000022-2-200000000000000000000000000000000000
χ434444-4-4-2-2-222-2-2-222-2-214-42211-1-1-1-11-2-200-2220000−2i3−2i32i32i311-1-1i3i3−i3−i3i3i3−i3−i3000000000000000000000000000
χ444444-4-4-2-2-222-2-2-222-2-214-42211-1-1-1-11-2-200-22200002i32i3−2i3−2i311-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000000000000
χ454444-4-4-2-2-222-2-2-222-2-21-442211-1-1-1-1122002-2-200000000-1-11133-3-3-3-333000000000000000000000000000
χ464444-4-4-2-2-222-2-2-222-2-21-442211-1-1-1-1122002-2-200000000-1-111-3-33333-3-3000000000000000000000000000
χ4744-4-40044-40044-400-4-440000-440000-4000000000000000000000000000000002i−2i0000002i−2i2i−2i0000000000
χ4844-4-40044-40044-400-4-440000-440000-400000000000000000000000000000000−2i2i000000−2i2i−2i2i0000000000
χ4944-4-400-242−2i32i34-22−2i32i3-4-4-200002-2−2i32i3−2i32i32000000000000000000000000000000002i−2i0000002ζ14−2ζ142ζ22−2ζ220000000000
χ5044-4-400-242−2i32i34-22−2i32i3-4-4-200002-2−2i32i3−2i32i3200000000000000000000000000000000−2i2i000000−2ζ142ζ14−2ζ222ζ220000000000
χ5144-4-400-2422i3−2i34-222i3−2i3-4-4-200002-22i3−2i32i3−2i32000000000000000000000000000000002i−2i0000002ζ22−2ζ222ζ14−2ζ140000000000
χ5244-4-400-2422i3−2i34-222i3−2i3-4-4-200002-22i3−2i32i3−2i3200000000000000000000000000000000−2i2i000000−2ζ222ζ22−2ζ142ζ140000000000
χ534-44-40044-400-4-4400-4440000-4-400004002-20002-22-22-22-200002-22-22-22-2000000000000000000000000000
χ544-44-40044-400-4-4400-4440000-4-40000400-22000-22-22-22-220000-22-22-22-22000000000000000000000000000
χ554-44-4004-2-4002-44002-2-20000220000-2−2i32i32-20002-22-2−1−i31+i3−1+i31−i3−2i32i300−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3000000000000000000000000000
χ564-44-4004-2-4002-44002-2-20000220000-2−2i32i3-22000-22-221+i3−1−i31−i3−1+i3−2i32i3001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3000000000000000000000000000
χ574-44-4004-2-4002-44002-2-20000220000-22i3−2i32-20002-22-2−1+i31−i3−1−i31+i32i3−2i300−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3000000000000000000000000000
χ584-44-4004-2-4002-44002-2-20000220000-22i3−2i3-22000-22-221−i3−1+i31+i3−1−i32i3−2i3001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3000000000000000000000000000
χ594-44-400-242−2i32i3-42-22i3−2i3-44-2000022−2i32i32i3−2i3-2002-2000−1+i31−i3−1−i31+i32-22-20000−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i3000000000000000000000000000
χ604-44-400-242−2i32i3-42-22i3−2i3-44-2000022−2i32i32i3−2i3-200-220001−i3−1+i31+i3−1−i3-22-2200001−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i3000000000000000000000000000
χ614-44-400-2422i3−2i3-42-2−2i32i3-44-20000222i3−2i3−2i32i3-2002-2000−1−i31+i3−1+i31−i32-22-20000−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i3000000000000000000000000000
χ624-44-400-2422i3−2i3-42-2−2i32i3-44-20000222i3−2i3−2i32i3-200-220001+i3−1−i31−i3−1+i3-22-2200001+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i3000000000000000000000000000
χ634-44-400-2-22−2i32i322-22i3−2i32-210000-1-1i3−i3−i3i31−2i32i32-2000−1+i31−i3−1−i31+i3−1−i31+i3−1+i31−i3i3−i33-3-112−i3−2+i32+i3−2−i3-11000000000000000000000000000
χ644-44-400-2-22−2i32i322-22i3−2i32-210000-1-1i3−i3−i3i31−2i32i3-220001−i3−1+i31+i3−1−i31+i3−1−i31−i3−1+i3i3−i33-31-1−2+i32−i3−2−i32+i31-1000000000000000000000000000
χ654-44-400-2-22−2i32i322-22i3−2i32-210000-1-1i3−i3−i3i312i3−2i32-2000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3−i3i3-332−i3−2+i3-11-112+i3−2−i3000000000000000000000000000
χ664-44-400-2-22−2i32i322-22i3−2i32-210000-1-1i3−i3−i3i312i3−2i3-220001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3−i3i3-33−2+i32−i31-11-1−2−i32+i3000000000000000000000000000
χ674-44-400-2-222i3−2i322-2−2i32i32-210000-1-1−i3i3i3−i31−2i32i32-2000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3i3−i3-332+i3−2−i3-11-112−i3−2+i3000000000000000000000000000
χ684-44-400-2-222i3−2i322-2−2i32i32-210000-1-1−i3i3i3−i31−2i32i3-220001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3i3−i3-33−2−i32+i31-11-1−2+i32−i3000000000000000000000000000
χ694-44-400-2-222i3−2i322-2−2i32i32-210000-1-1−i3i3i3−i312i3−2i32-2000−1−i31+i3−1+i31−i3−1+i31−i3−1−i31+i3−i3i33-3-112+i3−2−i32−i3−2+i3-11000000000000000000000000000
χ704-44-400-2-222i3−2i322-2−2i32i32-210000-1-1−i3i3i3−i312i3−2i3-220001+i3−1−i31−i3−1+i31−i3−1+i31+i3−1−i3−i3i33-31-1−2−i32+i3−2+i32−i31-1000000000000000000000000000
χ714-4-444-44-24442-4-4-4-4-22-200-22-22-2-2222000000000000000000000000000000000000−2i22i2000000i2−i2i2−i2000000
χ724-4-444-44-24442-4-4-4-4-22-200-22-22-2-22220000000000000000000000000000000000002i2−2i2000000−i2i2−i2i2000000
χ734-4-444-4-24-2-2-2-422224-4-2004-4-22-2-22220000000000000000000000000004-400000-22000000000000000000
χ744-4-444-4-24-2-2-2-422224-4-2004-4-22-2-2222000000000000000000000000000-44000002-2000000000000000000
χ754-4-44-44444-4-4-4-4-4444-4400-444-4-4-444-4000000000000000000000000000000000000000000000000000000
χ764-4-44-444-24-4-42-4-444-22-2002-2-2222-2-22000000000000000000000000000000000000000000006−6−66000000
χ774-4-44-444-24-4-42-4-444-22-2002-2-2222-2-2200000000000000000000000000000000000000000000−666−6000000
χ784-4-44-44-24-222-422-2-24-4-200-44-2222-2-220000000000000000000000000000000000000023−2300000000000000
χ794-4-44-44-24-222-422-2-24-4-200-44-2222-2-2200000000000000000000000000000000000000−232300000000000000
χ8088-8-8008-4-800-48-80044-400004-400004000000000000000000000000000000000000000000000000000000
χ8188-8-800-4-44−4i34i3-4-44−4i34i34420000-222i3−2i32i3−2i3-2000000000000000000000000000000000000000000000000000000
χ8288-8-800-4-444i3−4i3-4-444i3−4i34420000-22−2i32i3−2i32i3-2000000000000000000000000000000000000000000000000000000
χ838-8-888-8-4-4-4-4-444444-44200-442-222-2-2-2000000000000000000000000000000000000000000000000000000
χ848-8-88-88-4-4-444444-4-4-442004-42-2-2-222-2000000000000000000000000000000000000000000000000000000

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