Finite Group Databasebeta

← Group #11778702

Character table — Group #11778702

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444448888888888888888888888888121224242424242424242424242424242424242424484872727272
order1222223366666666663446666666661212441212121212121212121212121212121212121212121212224444466881212121212122424242412124488
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
χ511111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1
χ611111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-11-1-1-11111-1-1-1-1111111-1-1-1-111
χ711111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-11111-1-1-1-1-1-111-1-111
χ811111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-111-1-1
χ92222222222222222222-2-2222222222-2-200-2-2-200000000-2-2-2-200000000220-200022000000-2-20000000000
χ102222222222222222222-2-2222222222-2-200-2-2-200000000-2-2-2-200000000-2-202000-2-2000000220000000000
χ112222222-12-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-12222-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12202022-1-100-1-1-1-1-1-10000000000
χ122222222-12-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-12222-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20-20-2-211001111110000000000
χ132222222-12-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-122-2-2-1-12-2-2-2-21111-1-1-1-11111111122020-2-2-1-1001111-1-10000000000
χ142222222-12-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-122-2-2-1-12-2-2-2-21111-1-1-1-111111111-2-20-20221100-1-1-1-1110000000000
χ152222222-12-1-1-1-1-1-122-1-1-2-222-1-1-1-1-1-1-1-2-20011-20000−i3−i3i3i31111−i3−i3−i3−i3i3i3i3i3220-2000-1-100−i3−i3i3i3110000000000
χ162222222-12-1-1-1-1-1-122-1-1-2-222-1-1-1-1-1-1-1-2-20011-20000−i3−i3i3i31111−i3−i3−i3−i3i3i3i3i3-2-2020001100i3i3−i3−i3-1-10000000000
χ172222222-12-1-1-1-1-1-122-1-1-2-222-1-1-1-1-1-1-1-2-20011-20000i3i3−i3−i31111i3i3i3i3−i3−i3−i3−i3220-2000-1-100i3i3−i3−i3110000000000
χ182222222-12-1-1-1-1-1-122-1-1-2-222-1-1-1-1-1-1-1-2-20011-20000i3i3−i3−i31111i3i3i3i3−i3−i3−i3−i3-2-2020001100−i3−i3i3i3-1-10000000000
χ19222222-12-1222222-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100202000022000000-1-1-1-1-1-10000
χ20222222-12-1222222-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-20-20000-2-20000001111110000
χ21222222-12-1222222-1-12-122-1-1-1-1-1-1-1-1-1-1-1-2-222-11111-2-2-2-2-1-1-1-111111111002020000-2-20000001111-1-10000
χ22222222-12-1222222-1-12-122-1-1-1-1-1-1-1-1-1-1-1-2-222-11111-2-2-2-2-1-1-1-11111111100-20-2000022000000-1-1-1-1110000
χ232222-2-22222-2-22-2-222222-2-2-22-2-2-2-22222002-2-20000000022-2-2000000000020-200000000000000002-20000
χ242222-2-22222-2-22-2-222222-2-2-22-2-2-2-22222002-2-20000000022-2-20000000000-2020000000000000000-220000
χ252222-2-22222-2-22-2-22222-22-2-22-2-2-2-222-2-200-22200000000-2-22200000000000000000000000000000002-200
χ262222-2-22222-2-22-2-22222-22-2-22-2-2-2-222-2-200-22200000000-2-2220000000000000000000000000000000-2200
χ272222-2-2-12-12-2-22-2-2-1-12-12-211-11111-1-1-1-1002-21−i3−i3i3i30000-1-111−i3−i3i3i3−i3−i3i3i30020-2000000000000−i3−i3i3i3-110000
χ282222-2-2-12-12-2-22-2-2-1-12-12-211-11111-1-1-1-1002-21−i3−i3i3i30000-1-111−i3−i3i3i3−i3−i3i3i300-202000000000000i3i3−i3−i31-10000
χ292222-2-2-12-12-2-22-2-2-1-12-12-211-11111-1-1-1-1002-21i3i3−i3−i30000-1-111i3i3−i3−i3i3i3−i3−i30020-2000000000000i3i3−i3−i3-110000
χ302222-2-2-12-12-2-22-2-2-1-12-12-211-11111-1-1-1-1002-21i3i3−i3−i30000-1-111i3i3−i3−i3i3i3−i3−i300-202000000000000−i3−i3i3i31-10000
χ3122-2-22-2222222-2-2-2-2-2-22002-2222-2-2-2-20000000000000000000000000002-2000002-22−20000002−22−200002−2
χ3222-2-22-2222222-2-2-2-2-2-22002-2222-2-2-2-20000000000000000000000000002-2000002-2−22000000−22−220000−22
χ3322-2-22-2222222-2-2-2-2-2-22002-2222-2-2-2-2000000000000000000000000000-2200000-222−20000002−22−20000−22
χ3422-2-22-2222222-2-2-2-2-2-22002-2222-2-2-2-2000000000000000000000000000-2200000-22−22000000−22−2200002−2
χ35444444-24-2444444-2-24-2-4-4-2-2-2-2-2-2-2-2-22200-4-4200000000222200000000000000000000000000000000000
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
χ38444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-2-2111111122002220000−2i3−2i32i32i3-1-1-1-1i3i3i3i3−i3−i3−i3−i3000000000000000000000000000
χ39444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-2-21111111220022200002i32i3−2i3−2i3-1-1-1-1−i3−i3−i3−i3i3i3i3i3000000000000000000000000000
χ404444-4-44-24-222-22244-2-24-4-4-4-22222-2-24400-22-400000000-2-22200000000000000000000000000000000000
χ414444-4-44-24-222-22244-2-2-44-4-4-22222-2-2-4-4002-240000000022-2-200000000000000000000000000000000000
χ424444-4-4-24-24-4-44-4-4-2-24-2-4422-22222-2-22200-44-20000000022-2-200000000000000000000000000000000000
χ434444-4-4-2-2-2-222-222-2-2-214-4221-1-1-1-111-2-200-222−2i3−2i32i32i3000011-1-1i3i3−i3−i3i3i3−i3−i3000000000000000000000000000
χ444444-4-4-2-2-2-222-222-2-2-214-4221-1-1-1-111-2-200-2222i32i3−2i3−2i3000011-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000000000000
χ454444-4-4-2-2-2-222-222-2-2-21-44221-1-1-1-11122002-2-200000000-1-11133-3-3-3-333000000000000000000000000000
χ464444-4-4-2-2-2-222-222-2-2-21-44221-1-1-1-11122002-2-200000000-1-111-3-33333-3-3000000000000000000000000000
χ4744-4-44-44-24-2-2-2222-4-42-2004-4-2-2-222220000000000000000000000000004-400000-22000000000000000000
χ4844-4-44-44-24-2-2-2222-4-42-2004-4-2-2-22222000000000000000000000000000-44000002-2000000000000000000
χ4944-4-44-4-24-2444-4-4-422-4-200-22-2-2-2222200000000000000000000000000000000000022−22000000−22−22000000
χ5044-4-44-4-24-2444-4-4-422-4-200-22-2-2-22222000000000000000000000000000000000000−22220000002−22−2000000
χ5144-4-4-444444-4-4-444-4-4-4400-444-4-444-4-4000000000000000000000000000000000000000000000000000000
χ5244-4-4-444-24-2222-2-2-4-42-200-44-222-2-22200000000000000000000000000000000000000000023−230000000000
χ5344-4-4-444-24-2222-2-2-4-42-200-44-222-2-222000000000000000000000000000000000000000000−23230000000000
χ5444-4-4-44-24-24-4-4-44422-4-2002-2-222-2-22200000000000000000000000000000000000000000000i6−i6−i6i6000000
χ5544-4-4-44-24-24-4-4-44422-4-2002-2-222-2-22200000000000000000000000000000000000000000000−i6i6i6−i6000000
χ564-44-40044-4-4004004-4-440000-400004-4002i−2i0002i−2i2i−2i2i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i000000000000000000000000000
χ574-44-40044-4-4004004-4-440000-400004-400−2i2i000−2i2i−2i2i−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000
χ584-44-4004-2-42−2i32i3-2−2i32i34-42-200002−2i32i3−2i32i3-22002i−2i0002i−2i2i−2i2ζ14−2ζ142ζ22−2ζ2200002ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ22000000000000000000000000000
χ594-44-4004-2-42−2i32i3-2−2i32i34-42-200002−2i32i3−2i32i3-2200−2i2i000−2i2i−2i2i−2ζ142ζ14−2ζ222ζ220000−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22000000000000000000000000000
χ604-44-4004-2-422i3−2i3-22i3−2i34-42-2000022i3−2i32i3−2i3-22002i−2i0002i−2i2i−2i2ζ22−2ζ222ζ14−2ζ1400002ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ14000000000000000000000000000
χ614-44-4004-2-422i3−2i3-22i3−2i34-42-2000022i3−2i32i3−2i3-2200−2i2i000−2i2i−2i2i−2ζ222ζ22−2ζ142ζ140000−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14000000000000000000000000000
χ624-44-400-242-400400-22-4-2000020000-22−2i32i32i−2i0002ζ14−2ζ142ζ22−2ζ222i−2i2i−2i−2i32i3002ζ14−2ζ142ζ22−2ζ222ζ14−2ζ142ζ22−2ζ22000000000000000000000000000
χ634-44-400-242-400400-22-4-2000020000-22−2i32i3−2i2i000−2ζ142ζ14−2ζ222ζ22−2i2i−2i2i−2i32i300−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22000000000000000000000000000
χ644-44-400-242-400400-22-4-2000020000-222i3−2i32i−2i0002ζ22−2ζ222ζ14−2ζ142i−2i2i−2i2i3−2i3002ζ22−2ζ222ζ14−2ζ142ζ22−2ζ222ζ14−2ζ14000000000000000000000000000
χ654-44-400-242-400400-22-4-2000020000-222i3−2i3−2i2i000−2ζ222ζ22−2ζ142ζ14−2i2i−2i2i2i3−2i300−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14000000000000000000000000000
χ664-44-400-2-222−2i32i3-2−2i32i3-22210000-1i3−i3i3−i31-1−2i32i32i−2i0002ζ14−2ζ142ζ22−2ζ222ζ14−2ζ142ζ22−2ζ22i3−i33-3−3ζ14−ζ223ζ14+ζ22−ii−ii−ζ14−3ζ22ζ14+3ζ22000000000000000000000000000
χ674-44-400-2-222−2i32i3-2−2i32i3-22210000-1i3−i3i3−i31-1−2i32i3−2i2i000−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22i3−i33-33ζ14+ζ22−3ζ14−ζ22i−ii−iζ14+3ζ22−ζ14−3ζ22000000000000000000000000000
χ684-44-400-2-222−2i32i3-2−2i32i3-22210000-1i3−i3i3−i31-12i3−2i32i−2i0002ζ22−2ζ222ζ14−2ζ142ζ14−2ζ142ζ22−2ζ22−i3i3-33−ii−3ζ14−ζ223ζ14+ζ22−ζ14−3ζ22ζ14+3ζ22−ii000000000000000000000000000
χ694-44-400-2-222−2i32i3-2−2i32i3-22210000-1i3−i3i3−i31-12i3−2i3−2i2i000−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−i3i3-33i−i3ζ14+ζ22−3ζ14−ζ22ζ14+3ζ22−ζ14−3ζ22i−i000000000000000000000000000
χ704-44-400-2-2222i3−2i3-22i3−2i3-22210000-1−i3i3−i3i31-1−2i32i32i−2i0002ζ14−2ζ142ζ22−2ζ222ζ22−2ζ222ζ14−2ζ14i3−i3-33−ii−ζ14−3ζ22ζ14+3ζ22−3ζ14−ζ223ζ14+ζ22−ii000000000000000000000000000
χ714-44-400-2-2222i3−2i3-22i3−2i3-22210000-1−i3i3−i3i31-1−2i32i3−2i2i000−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14i3−i3-33i−iζ14+3ζ22−ζ14−3ζ223ζ14+ζ22−3ζ14−ζ22i−i000000000000000000000000000
χ724-44-400-2-2222i3−2i3-22i3−2i3-22210000-1−i3i3−i3i31-12i3−2i32i−2i0002ζ22−2ζ222ζ14−2ζ142ζ22−2ζ222ζ14−2ζ14−i3i33-3−ζ14−3ζ22ζ14+3ζ22−ii−ii−3ζ14−ζ223ζ14+ζ22000000000000000000000000000
χ734-44-400-2-2222i3−2i3-22i3−2i3-22210000-1−i3i3−i3i31-12i3−2i3−2i2i000−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14−i3i33-3ζ14+3ζ22−ζ14−3ζ22i−ii−i3ζ14+ζ22−3ζ14−ζ22000000000000000000000000000
χ744-4-440044-4-400-400-44440000-40000-44000000000000000000000000000000002-200002-22-2000000000000
χ754-4-440044-4-400-400-44440000-40000-4400000000000000000000000000000000-220000-22-22000000000000
χ764-4-44004-2-42−2i32i322i3−2i3-44-2-200002−2i32i32i3−2i32-2000000000000000000000000000000002-20000−1+i31−i3−1−i31+i3000000000000
χ774-4-44004-2-42−2i32i322i3−2i3-44-2-200002−2i32i32i3−2i32-200000000000000000000000000000000-2200001−i3−1+i31+i3−1−i3000000000000
χ784-4-44004-2-422i3−2i32−2i32i3-44-2-2000022i3−2i3−2i32i32-2000000000000000000000000000000002-20000−1−i31+i3−1+i31−i3000000000000
χ794-4-44004-2-422i3−2i32−2i32i3-44-2-2000022i3−2i3−2i32i32-200000000000000000000000000000000-2200001+i3−1−i31−i3−1+i3000000000000
χ8088-8-88-8-4-4-4-4-4-4444444200-44222-2-2-2-2000000000000000000000000000000000000000000000000000000
χ8188-8-8-88-4-4-4-4444-4-44442004-42-2-222-2-2000000000000000000000000000000000000000000000000000000
χ828-8-8800-484-800-8004-48-40000400004-4000000000000000000000000000000000000000000000000000000
χ838-8-8800-4-444−4i34i344i3−4i34-4-420000-22i3−2i3−2i32i3-22000000000000000000000000000000000000000000000000000000
χ848-8-8800-4-4444i3−4i34−4i34i34-4-420000-2−2i32i32i3−2i3-22000000000000000000000000000000000000000000000000000000

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