Finite Group Databasebeta

← Group #11778588

Character table — Group #11778588

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444448888888888888888888888888121224242424242424242424242424242424242424484872727272
order122222336666666666344666666666121244121212121212121212121212121212121212121212121244444448812121212121212122424242412124488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-11-111-1-111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-11-11-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111-11-1-1-111-1-1-1-111111111-1-1-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-1-1-1-1-111-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1
χ92222222222222222222-2-2222222222-2-2000000-2-2-20000-2-2-2-200000000220-2000000000-2-2220000000000
χ102222222222222222222-2-2222222222-2-2000000-2-2-20000-2-2-2-200000000-2-20200000000022-2-20000000000
χ112222222-1222-122-12-12-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-100202002200000000-1-1-1-1-1-10000
χ122222222-1222-122-12-12-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-100-20-200-2-2000000001111110000
χ132222222-1222-122-12-12-122-1-1-1-1-1-1-1-1-1-1-1-2-2111122-1-2-2-2-2-1-1-1-1111111110020200-2-2000000001111-1-10000
χ142222222-1222-122-12-12-122-1-1-1-1-1-1-1-1-1-1-1-2-2111122-1-2-2-2-2-1-1-1-11111111100-20-2002200000000-1-1-1-1110000
χ15222222-12-1-1-12-1-12-12-1-12222-1-1-1-1-1-1-122222222-1-12-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1220202200-1-1-1-1-1-1-1-10000000000
χ16222222-12-1-1-12-1-12-12-1-12222-1-1-1-1-1-1-122222222-1-12-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20-20-2-200111111110000000000
χ17222222-12-1-1-12-1-12-12-1-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-1-121111-1-1-1-11111111122020-2-2001111-1-1-1-10000000000
χ18222222-12-1-1-12-1-12-12-1-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-1-121111-1-1-1-111111111-2-20-202200-1-1-1-111110000000000
χ19222222-12-1-1-12-1-12-12-1-1-2-222-1-1-1-1-1-1-1-2-200000011-2−i3−i3i3i31111−i3−i3−i3−i3i3i3i3i3220-200000−i3−i3i3i311-1-10000000000
χ20222222-12-1-1-12-1-12-12-1-1-2-222-1-1-1-1-1-1-1-2-200000011-2−i3−i3i3i31111−i3−i3−i3−i3i3i3i3i3-2-20200000i3i3−i3−i3-1-1110000000000
χ21222222-12-1-1-12-1-12-12-1-1-2-222-1-1-1-1-1-1-1-2-200000011-2i3i3−i3−i31111i3i3i3i3−i3−i3−i3−i3220-200000i3i3−i3−i311-1-10000000000
χ22222222-12-1-1-12-1-12-12-1-1-2-222-1-1-1-1-1-1-1-2-200000011-2i3i3−i3−i31111i3i3i3i3−i3−i3−i3−i3-2-20200000−i3−i3i3i3-1-1110000000000
χ232222-2-2222-2-22-2-2222222-2-2-22-2-2-2-222220000002-2-2000022-2-2000000000020-200000000000000002-20000
χ242222-2-2222-2-22-2-2222222-2-2-22-2-2-2-222220000002-2-2000022-2-20000000000-2020000000000000000-220000
χ252222-2-2222-2-22-2-222222-22-2-22-2-2-2-222-2-2000000-2220000-2-22200000000000000000000000000000002-200
χ262222-2-2222-2-22-2-222222-22-2-22-2-2-2-222-2-2000000-2220000-2-2220000000000000000000000000000000-2200
χ272222-2-22-12-2-2-1-2-2-12-12-12-211-11111-1-1-1-100−i3−i3i3i32-210000-1-111−i3−i3i3i3−i3−i3i3i30020-2000000000000−i3−i3i3i3-110000
χ282222-2-22-12-2-2-1-2-2-12-12-12-211-11111-1-1-1-100−i3−i3i3i32-210000-1-111−i3−i3i3i3−i3−i3i3i300-202000000000000i3i3−i3−i31-10000
χ292222-2-22-12-2-2-1-2-2-12-12-12-211-11111-1-1-1-100i3i3−i3−i32-210000-1-111i3i3−i3−i3i3i3−i3−i30020-2000000000000i3i3−i3−i3-110000
χ302222-2-22-12-2-2-1-2-2-12-12-12-211-11111-1-1-1-100i3i3−i3−i32-210000-1-111i3i3−i3−i3i3i3−i3−i300-202000000000000−i3−i3i3i31-10000
χ3122-2-2-2222-2-2-2222-2-2-222002-2-222-2-2-220000000000000000000000000002-200000−i2i20000002-2−i2i2−i2i20000−i2i2
χ3222-2-2-2222-2-2-2222-2-2-222002-2-222-2-2-220000000000000000000000000002-200000i2−i20000002-2i2−i2i2−i20000i2−i2
χ3322-2-2-2222-2-2-2222-2-2-222002-2-222-2-2-22000000000000000000000000000-2200000−i2i2000000-22−i2i2−i2i20000i2−i2
χ3422-2-2-2222-2-2-2222-2-2-222002-2-222-2-2-22000000000000000000000000000-2200000i2−i2000000-22i2−i2i2−i20000−i2i2
χ354444444-2444-244-24-24-2-4-4-2-2-2-2-2-2-2-2-222000000-4-420000222200000000000000000000000000000000000
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
χ37444444-2-2-2-2-2-2-2-2-2-2-2-2144-2-21111111-2-2-4-42222-2-2-222221111-1-1-1-1-1-1-1-1000000000000000000000000000
χ38444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-2-2111111122000000222−2i3−2i32i32i3-1-1-1-1i3i3i3i3−i3−i3−i3−i3000000000000000000000000000
χ39444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-2-21111111220000002222i32i3−2i3−2i3-1-1-1-1−i3−i3−i3−i3i3i3i3i3000000000000000000000000000
χ404444-4-44-24-4-4-2-4-4-24-24-2-4422-22222-2-222000000-44-2000022-2-200000000000000000000000000000000000
χ414444-4-4-24-2224224-24-2-24-4-4-4-22222-2-244000000-22-40000-2-22200000000000000000000000000000000000
χ424444-4-4-24-2224224-24-2-2-44-4-4-22222-2-2-4-40000002-24000022-2-200000000000000000000000000000000000
χ434444-4-4-2-2-222-222-2-2-2-214-4221-1-1-1-111-2-200−2i3−2i32i32i3-222000011-1-1i3i3−i3−i3i3i3−i3−i3000000000000000000000000000
χ444444-4-4-2-2-222-222-2-2-2-214-4221-1-1-1-111-2-2002i32i3−2i3−2i3-222000011-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000000000000
χ454444-4-4-2-2-222-222-2-2-2-21-44221-1-1-1-111220000002-2-20000-1-11133-3-3-3-333000000000000000000000000000
χ464444-4-4-2-2-222-222-2-2-2-21-44221-1-1-1-111220000002-2-20000-1-111-3-33333-3-3000000000000000000000000000
χ4744-4-44-444-4444-4-4-4-4-44400-44-4-4-444-44000000000000000000000000000000000000000000000000000000
χ4844-4-44-44-2-444-2-4-42-424-2002-2222-2-22-2000000000000000000000000000000000000000000006−6−66000000
χ4944-4-44-44-2-444-2-4-42-424-2002-2222-2-22-200000000000000000000000000000000000000000000−666−6000000
χ5044-4-44-4-242-2-2422-42-4-2-200-44222-2-22-2000000000000000000000000000000000000000023−23000000000000
χ5144-4-44-4-242-2-2422-42-4-2-200-44222-2-22-20000000000000000000000000000000000000000−2323000000000000
χ5244-4-4-444-2-4-4-4-2442-424-200-222-2-2222-20000000000000000000000000000000000−2i22i200000000i2−i2i2−i2000000
χ5344-4-4-444-2-4-4-4-2442-424-200-222-2-2222-200000000000000000000000000000000002i2−2i200000000−i2i2−i2i2000000
χ5444-4-4-44-242224-2-2-42-4-2-2004-42-2-2222-20000000000000000000000000004-40000000000000-220000000000
χ5544-4-4-44-242224-2-2-42-4-2-2004-42-2-2222-2000000000000000000000000000-4400000000000002-20000000000
χ564-44-40044400-4004-4-4-44000040000-4-4000000000000000000000000000000002-2002-22-200000000000000
χ574-44-40044400-4004-4-4-44000040000-4-400000000000000000000000000000000-2200-22-2200000000000000
χ584-44-400-24-2−2i32i3-4−2i32i342-42-20000-2−2i32i3−2i32i322000000000000000000000000000000002-200−1−i31+i3−1+i31−i300000000000000
χ594-44-400-24-2−2i32i3-4−2i32i342-42-20000-2−2i32i3−2i32i32200000000000000000000000000000000-22001+i3−1−i31−i3−1+i300000000000000
χ604-44-400-24-22i3−2i3-42i3−2i342-42-20000-22i3−2i32i3−2i322000000000000000000000000000000002-200−1+i31−i3−1−i31+i300000000000000
χ614-44-400-24-22i3−2i3-42i3−2i342-42-20000-22i3−2i32i3−2i32200000000000000000000000000000000-22001−i3−1+i31+i3−1−i300000000000000
χ624-4-440044-400-400-444-440000-400004-4002i−2i2i−2i2i−2i0002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i000000000000000000000000000
χ634-4-440044-400-400-444-440000-400004-400−2i2i−2i2i−2i2i000−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000
χ644-4-44004-2-40020024-2-4-2000020000-22−2i32i32i−2i2ζ14−2ζ142ζ22−2ζ220002i−2i2i−2i−2i32i3002ζ14−2ζ142ζ22−2ζ222ζ14−2ζ142ζ22−2ζ22000000000000000000000000000
χ654-4-44004-2-40020024-2-4-2000020000-22−2i32i3−2i2i−2ζ142ζ14−2ζ222ζ22000−2i2i−2i2i−2i32i300−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22000000000000000000000000000
χ664-4-44004-2-40020024-2-4-2000020000-222i3−2i32i−2i2ζ22−2ζ222ζ14−2ζ140002i−2i2i−2i2i3−2i3002ζ22−2ζ222ζ14−2ζ142ζ22−2ζ222ζ14−2ζ14000000000000000000000000000
χ674-4-44004-2-40020024-2-4-2000020000-222i3−2i3−2i2i−2ζ222ζ22−2ζ142ζ14000−2i2i−2i2i2i3−2i300−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14000000000000000000000000000
χ684-4-4400-242−2i32i3-42i3−2i3-4-242-2000022i3−2i3−2i32i3-22002i−2i2i−2i2i−2i0002ζ14−2ζ142ζ22−2ζ2200002ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ22000000000000000000000000000
χ694-4-4400-242−2i32i3-42i3−2i3-4-242-2000022i3−2i3−2i32i3-2200−2i2i−2i2i−2i2i000−2ζ142ζ14−2ζ222ζ220000−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22000000000000000000000000000
χ704-4-4400-2422i3−2i3-4−2i32i3-4-242-200002−2i32i32i3−2i3-22002i−2i2i−2i2i−2i0002ζ22−2ζ222ζ14−2ζ1400002ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ14000000000000000000000000000
χ714-4-4400-2422i3−2i3-4−2i32i3-4-242-200002−2i32i32i3−2i3-2200−2i2i−2i2i−2i2i000−2ζ222ζ22−2ζ142ζ140000−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14000000000000000000000000000
χ724-4-4400-2-22−2i32i322i3−2i32-2-2210000-1−i3i3i3−i31-1−2i32i32i−2i2ζ14−2ζ142ζ22−2ζ220002ζ14−2ζ142ζ22−2ζ22i3−i33-3−3ζ14−ζ223ζ14+ζ22−ii−ii−ζ14−3ζ22ζ14+3ζ22000000000000000000000000000
χ734-4-4400-2-22−2i32i322i3−2i32-2-2210000-1−i3i3i3−i31-1−2i32i3−2i2i−2ζ142ζ14−2ζ222ζ22000−2ζ142ζ14−2ζ222ζ22i3−i33-33ζ14+ζ22−3ζ14−ζ22i−ii−iζ14+3ζ22−ζ14−3ζ22000000000000000000000000000
χ744-4-4400-2-22−2i32i322i3−2i32-2-2210000-1−i3i3i3−i31-12i3−2i32i−2i2ζ22−2ζ222ζ14−2ζ140002ζ14−2ζ142ζ22−2ζ22−i3i3-33−ii−3ζ14−ζ223ζ14+ζ22−ζ14−3ζ22ζ14+3ζ22−ii000000000000000000000000000
χ754-4-4400-2-22−2i32i322i3−2i32-2-2210000-1−i3i3i3−i31-12i3−2i3−2i2i−2ζ222ζ22−2ζ142ζ14000−2ζ142ζ14−2ζ222ζ22−i3i3-33i−i3ζ14+ζ22−3ζ14−ζ22ζ14+3ζ22−ζ14−3ζ22i−i000000000000000000000000000
χ764-4-4400-2-222i3−2i32−2i32i32-2-2210000-1i3−i3−i3i31-1−2i32i32i−2i2ζ14−2ζ142ζ22−2ζ220002ζ22−2ζ222ζ14−2ζ14i3−i3-33−ii−ζ14−3ζ22ζ14+3ζ22−3ζ14−ζ223ζ14+ζ22−ii000000000000000000000000000
χ774-4-4400-2-222i3−2i32−2i32i32-2-2210000-1i3−i3−i3i31-1−2i32i3−2i2i−2ζ142ζ14−2ζ222ζ22000−2ζ222ζ22−2ζ142ζ14i3−i3-33i−iζ14+3ζ22−ζ14−3ζ223ζ14+ζ22−3ζ14−ζ22i−i000000000000000000000000000
χ784-4-4400-2-222i3−2i32−2i32i32-2-2210000-1i3−i3−i3i31-12i3−2i32i−2i2ζ22−2ζ222ζ14−2ζ140002ζ22−2ζ222ζ14−2ζ14−i3i33-3−ζ14−3ζ22ζ14+3ζ22−ii−ii−3ζ14−ζ223ζ14+ζ22000000000000000000000000000
χ794-4-4400-2-222i3−2i32−2i32i32-2-2210000-1i3−i3−i3i31-12i3−2i3−2i2i−2ζ222ζ22−2ζ142ζ14000−2ζ222ζ22−2ζ142ζ14−i3i33-3ζ14+3ζ22−ζ14−3ζ22i−ii−i3ζ14+ζ22−3ζ14−ζ22000000000000000000000000000
χ8088-8-88-8-4-44-4-4-444444-42004-4-2-2-222-22000000000000000000000000000000000000000000000000000000
χ8188-8-8-88-4-4444-4-4-4444-4200-44-222-2-2-22000000000000000000000000000000000000000000000000000000
χ828-88-8008-4800400-4-84-8-40000-4000044000000000000000000000000000000000000000000000000000000
χ838-88-800-4-4-4−4i34i34−4i34i3-44442000022i3−2i32i3−2i3-2-2000000000000000000000000000000000000000000000000000000
χ848-88-800-4-4-44i3−4i344i3−4i3-4444200002−2i32i3−2i32i3-2-2000000000000000000000000000000000000000000000000000000

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