Finite Group Databasebeta

← Group #11778826

Character table — Group #11778826

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444448888888888888888888888888121224242424242424242424242424242424242424484872727272
order122222336666666666344666666666121244121212121212121212121212121212121212121212121244444448812121212121212122424242412124488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-111-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-11-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111
χ811111111111111111111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111111111-1-111-1-1
χ92222222222222222222-2-2222222222-2-2000000-2-2-2-2-2-2-200000000000022-200000022-2-200000000000000
χ102222222222222222222-2-2222222222-2-2000000-2-2-2-2-2-2-2000000000000-2-22000000-2-22200000000000000
χ112222222-122-1222-12-12-122-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100020022200000000-1-1-1-1-1-10000
χ122222222-122-1222-12-12-122-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000-200-2-2-2000000001111110000
χ132222222-122-1222-12-12-122-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222-1-1-1-1-11111111111110002002-2-2000000001111-1-10000
χ142222222-122-1222-12-12-122-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222-1-1-1-1-1111111111111000-200-22200000000-1-1-1-1110000
χ15222222-12-1-12-1-1-12-12-1-1222-1-1-1-12-1-1-12222-1-1-1-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-1222022000-1-1-1-1-1-1-1-10000000000
χ16222222-12-1-12-1-1-12-12-1-1222-1-1-1-12-1-1-12222-1-1-1-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-20-2-2000111111110000000000
χ17222222-12-1-12-1-1-12-12-1-1222-1-1-1-12-1-1-122-2-21111-1-12-1-1-1-1-2-2-2-2111111112220-2-2000-1-1-1-111110000000000
χ18222222-12-1-12-1-1-12-12-1-1222-1-1-1-12-1-1-122-2-21111-1-12-1-1-1-1-2-2-2-211111111-2-2-20220001111-1-1-1-10000000000
χ19222222-12-1-12-1-1-12-12-1-1-2-22-1-1-1-12-1-1-1-2-200−i3−i3i3i311-211110000−i3−i3−i3−i3i3i3i3i322-2000000-1-111−i3−i3i3i30000000000
χ20222222-12-1-12-1-1-12-12-1-1-2-22-1-1-1-12-1-1-1-2-200−i3−i3i3i311-211110000−i3−i3−i3−i3i3i3i3i3-2-2200000011-1-1i3i3−i3−i30000000000
χ21222222-12-1-12-1-1-12-12-1-1-2-22-1-1-1-12-1-1-1-2-200i3i3−i3−i311-211110000i3i3i3i3−i3−i3−i3−i322-2000000-1-111i3i3−i3−i30000000000
χ22222222-12-1-12-1-1-12-12-1-1-2-22-1-1-1-12-1-1-1-2-200i3i3−i3−i311-211110000i3i3i3i3−i3−i3−i3−i3-2-2200000011-1-1−i3−i3i3i30000000000
χ232222-2-222-2-22-2-22222222-2-222-2-2-22-2-2220000002-2-222-2-2000000000000000000000000000000000002-200
χ242222-2-222-2-22-2-22222222-2-222-2-2-22-2-2220000002-2-222-2-200000000000000000000000000000000000-2200
χ252222-2-222-2-22-2-2222222-22-222-2-2-22-2-2-2-2000000-222-2-222000000000000000200-200000000000000-220000
χ262222-2-222-2-22-2-2222222-22-222-2-2-22-2-2-2-2000000-222-2-222000000000000000-2002000000000000002-20000
χ272222-2-22-1-2-2-1-2-22-12-12-1-221-1-1111-11111000000-22-111-1-133−3−333−3−333−3−3000200-2000000000033−3−31-10000
χ282222-2-22-1-2-2-1-2-22-12-12-1-221-1-1111-11111000000-22-111-1-133−3−333−3−333−3−3000-20020000000000−3−333-110000
χ292222-2-22-1-2-2-1-2-22-12-12-1-221-1-1111-11111000000-22-111-1-1−3−333−3−333−3−333000200-20000000000−3−3331-10000
χ302222-2-22-1-2-2-1-2-22-12-12-1-221-1-1111-11111000000-22-111-1-1−3−333−3−333−3−333000-2002000000000033−3−3-110000
χ3122-2-22-222222-2-22-2-2-2-220022-222-2-2-2-20000000000000000000000000002-2000002−22-20000002−22−200002−2
χ3222-2-22-222222-2-22-2-2-2-220022-222-2-2-2-20000000000000000000000000002-200000−222-2000000−22−220000−22
χ3322-2-22-222222-2-22-2-2-2-220022-222-2-2-2-2000000000000000000000000000-22000002−2-220000002−22−20000−22
χ3422-2-22-222222-2-22-2-2-2-220022-222-2-2-2-2000000000000000000000000000-2200000−22-22000000−22−2200002−2
χ354444444-244-2444-24-24-2-4-4-2-2-2-2-2-2-2-2-222000000-4-422222000000000000000000000000000000000000000
χ36444444-2-2-2-2-2-2-2-2-2-2-2-2144-21111-2111-2-244-2-2-2-2-2-2-21111-2-2-2-211111111000000000000000000000000000
χ37444444-2-2-2-2-2-2-2-2-2-2-2-2144-21111-2111-2-2-4-42222-2-2-211112222-1-1-1-1-1-1-1-1000000000000000000000000000
χ38444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-21111-21112200−2i3−2i32i32i3222-1-1-1-10000i3i3i3i3−i3−i3−i3−i3000000000000000000000000000
χ39444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-21111-211122002i32i3−2i3−2i3222-1-1-1-10000−i3−i3−i3−i3i3i3i3i3000000000000000000000000000
χ404444-4-44-2-4-4-2-4-44-24-24-24-42-2-2222-222-2-20000004-42-2-222000000000000000000000000000000000000000
χ414444-4-4-2422422-24-24-2-24-4-4-2-222-4-22244000000-22-4-2-222000000000000000000000000000000000000000
χ424444-4-4-2422422-24-24-2-2-44-4-2-222-4-222-4-40000002-2422-2-2000000000000000000000000000000000000000
χ434444-4-4-2-222-222-2-2-2-2-214-4211-1-121-1-1-2-2000000-22211-1-100003i3i−3i−3i−3i−3i3i3i000000000000000000000000000
χ444444-4-4-2-222-222-2-2-2-2-214-4211-1-121-1-1-2-2000000-22211-1-10000−3i−3i3i3i3i3i−3i−3i000000000000000000000000000
χ454444-4-4-2-222-222-2-2-2-2-21-44211-1-121-1-1220000002-2-2-1-1112323−23−23−3−333−3−333000000000000000000000000000
χ464444-4-4-2-222-222-2-2-2-2-21-44211-1-121-1-1220000002-2-2-1-111−23−23232333−3−333−3−3000000000000000000000000000
χ4744-4-44-44-244-2-4-442-42-4-200-2-22-2-22222000000000000000000000000000000000022−2200000000−22−22000000
χ4844-4-44-44-244-2-4-442-42-4-200-2-22-2-222220000000000000000000000000000000000−2222000000002−22−2000000
χ4944-4-44-4-24-2-2422-2-42-42-2004-22-2-2-42220000000000000000000000000004-40000000-220000000000000000
χ5044-4-44-4-24-2-2422-2-42-42-2004-22-2-2-4222000000000000000000000000000-4400000002-20000000000000000
χ5144-4-4-4444-4-44444-4-4-4-4400-44-4-4-44-444000000000000000000000000000000000000000000000000000000
χ5244-4-4-444-2-4-4-24442-42-4-2002-2222-22-2-2000000000000000000000000000000000000000000006−6−66000000
χ5344-4-4-444-2-4-4-24442-42-4-2002-2222-22-2-200000000000000000000000000000000000000000000−666−6000000
χ5444-4-4-44-24224-2-2-2-42-42-200-4-222242-2-20000000000000000000000000000000000000023−2300000000000000
χ5544-4-4-44-24224-2-2-2-42-42-200-4-222242-2-200000000000000000000000000000000000000−232300000000000000
χ564-44-4004400-400-4-444-44000-4-400040000000000000000000000000000000002i−2i00000002i−2i2i−2i0000000000
χ574-44-4004400-400-4-444-44000-4-40004000000000000000000000000000000000−2i2i0000000−2i2i−2i2i0000000000
χ584-44-400-24−2i32i3-4−2i32i32-4-242-200022−2i32i30-2−2i32i300000000000000000000000000000002i−2i00000002ζ14−2ζ142ζ22−2ζ220000000000
χ594-44-400-24−2i32i3-4−2i32i32-4-242-200022−2i32i30-2−2i32i30000000000000000000000000000000−2i2i0000000−2ζ142ζ14−2ζ222ζ220000000000
χ604-44-400-242i3−2i3-42i3−2i32-4-242-2000222i3−2i30-22i3−2i300000000000000000000000000000002i−2i00000002ζ22−2ζ222ζ14−2ζ140000000000
χ614-44-400-242i3−2i3-42i3−2i32-4-242-2000222i3−2i30-22i3−2i30000000000000000000000000000000−2i2i0000000−2ζ222ζ22−2ζ142ζ140000000000
χ624-4-44004400-400-44-4-444000-44000-400002i−2i2i−2i2i−2i00000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000
χ634-4-44004400-400-44-4-444000-44000-40000−2i2i−2i2i−2i2i0000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000
χ644-4-44004-200200-4-2-424-20002-200020023−232i−2i2i−2i2i−2i00023−2300−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22000000000000000000000000000
χ654-4-44004-200200-4-2-424-20002-200020023−23−2i2i−2i2i−2i2i00023−2300ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000000000000000000000
χ664-4-44004-200200-4-2-424-20002-2000200−23232i−2i2i−2i2i−2i000−232300ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000000000000000000000
χ674-4-44004-200200-4-2-424-20002-2000200−2323−2i2i−2i2i−2i2i000−232300−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000000000000000000000
χ684-4-4400-24−2i32i3-42i3−2i3242-4-2-20002-2−2i32i3022i3−2i3002i−2i2ζ14−2ζ142ζ22−2ζ2200000002i−2i2i−2i2ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ22000000000000000000000000000
χ694-4-4400-24−2i32i3-42i3−2i3242-4-2-20002-2−2i32i3022i3−2i300−2i2i−2ζ142ζ14−2ζ222ζ220000000−2i2i−2i2i−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22000000000000000000000000000
χ704-4-4400-242i3−2i3-4−2i32i3242-4-2-20002-22i3−2i302−2i32i3002i−2i2ζ22−2ζ222ζ14−2ζ1400000002i−2i2i−2i2ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ14000000000000000000000000000
χ714-4-4400-242i3−2i3-4−2i32i3242-4-2-20002-22i3−2i302−2i32i300−2i2i−2ζ222ζ22−2ζ142ζ140000000−2i2i−2i2i−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14000000000000000000000000000
χ724-4-4400-2-2−2i32i322i3−2i32-222-21000-11i3−i30-1−i3i323−232i−2i2ζ14−2ζ142ζ22−2ζ22000−333i−3i−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14−2ζ20ζ4+ζ14+2ζ20ζ4−ζ14+2ζ20−ζ4+ζ14−2ζ202ζ4+ζ20−ζ22−2ζ4−ζ20+ζ22−2ζ4−ζ20−ζ222ζ4+ζ20+ζ22000000000000000000000000000
χ734-4-4400-2-2−2i32i322i3−2i32-222-21000-11i3−i30-1−i3i323−23−2i2i−2ζ142ζ14−2ζ222ζ22000−333i−3iζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14+2ζ20−ζ4−ζ14−2ζ20−ζ4+ζ14−2ζ20ζ4−ζ14+2ζ20−2ζ4−ζ20+ζ222ζ4+ζ20−ζ222ζ4+ζ20+ζ22−2ζ4−ζ20−ζ22000000000000000000000000000
χ744-4-4400-2-2−2i32i322i3−2i32-222-21000-11i3−i30-1−i3i3−23232i−2i2ζ14−2ζ142ζ22−2ζ220003−3−3i3iζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14+2ζ20−ζ4+ζ14−2ζ20−ζ4−ζ14−2ζ20ζ4+ζ14+2ζ20−2ζ4−ζ20−ζ222ζ4+ζ20+ζ222ζ4+ζ20−ζ22−2ζ4−ζ20+ζ22000000000000000000000000000
χ754-4-4400-2-2−2i32i322i3−2i32-222-21000-11i3−i30-1−i3i3−2323−2i2i−2ζ142ζ14−2ζ222ζ220003−3−3i3i−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14−2ζ20ζ4−ζ14+2ζ20ζ4+ζ14+2ζ20−ζ4−ζ14−2ζ202ζ4+ζ20+ζ22−2ζ4−ζ20−ζ22−2ζ4−ζ20+ζ222ζ4+ζ20−ζ22000000000000000000000000000
χ764-4-4400-2-22i3−2i32−2i32i32-222-21000-11−i3i30-1i3−i323−232i−2i2ζ22−2ζ222ζ14−2ζ14000−33−3i3i−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ222ζ4+ζ20−ζ22−2ζ4−ζ20+ζ22−2ζ4−ζ20−ζ222ζ4+ζ20+ζ22−ζ4−ζ14−2ζ20ζ4+ζ14+2ζ20ζ4−ζ14+2ζ20−ζ4+ζ14−2ζ20000000000000000000000000000
χ774-4-4400-2-22i3−2i32−2i32i32-222-21000-11−i3i30-1i3−i323−23−2i2i−2ζ222ζ22−2ζ142ζ14000−33−3i3iζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−2ζ4−ζ20+ζ222ζ4+ζ20−ζ222ζ4+ζ20+ζ22−2ζ4−ζ20−ζ22ζ4+ζ14+2ζ20−ζ4−ζ14−2ζ20−ζ4+ζ14−2ζ20ζ4−ζ14+2ζ20000000000000000000000000000
χ784-4-4400-2-22i3−2i32−2i32i32-222-21000-11−i3i30-1i3−i3−23232i−2i2ζ22−2ζ222ζ14−2ζ140003−33i−3iζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−2ζ4−ζ20−ζ222ζ4+ζ20+ζ222ζ4+ζ20−ζ22−2ζ4−ζ20+ζ22ζ4−ζ14+2ζ20−ζ4+ζ14−2ζ20−ζ4−ζ14−2ζ20ζ4+ζ14+2ζ20000000000000000000000000000
χ794-4-4400-2-22i3−2i32−2i32i32-222-21000-11−i3i30-1i3−i3−2323−2i2i−2ζ222ζ22−2ζ142ζ140003−33i−3i−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ222ζ4+ζ20+ζ22−2ζ4−ζ20−ζ22−2ζ4−ζ20+ζ222ζ4+ζ20−ζ22−ζ4+ζ14−2ζ20ζ4−ζ14+2ζ20ζ4+ζ14+2ζ20−ζ4−ζ14−2ζ20000000000000000000000000000
χ8088-8-88-8-4-4-4-4-444-44444200-42-2224-2-2-2000000000000000000000000000000000000000000000000000000
χ8188-8-8-88-4-444-4-4-4-4444420042-2-2-2-4-222000000000000000000000000000000000000000000000000000000
χ828-88-8008-400400-848-4-8-400044000-400000000000000000000000000000000000000000000000000000000
χ838-88-800-4-4−4i34i34−4i34i344-4-442000-2-22i3−2i3022i3−2i3000000000000000000000000000000000000000000000000000000
χ848-88-800-4-44i3−4i344i3−4i344-4-442000-2-2−2i32i302−2i32i3000000000000000000000000000000000000000000000000000000

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