Finite Group Databasebeta

← Group #11778401

Character table — Group #11778401

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444448888888888888888888888888121224242424242424242424242424242424242424484872727272
order1222223366666666663446666666661212441212121212121212121212121212121212121212121212442444466881212121212122424242412122488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111111111111-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111
χ811111111111111111111111111111111-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-111-1-1
χ92222222222222222222-2-2222222222-2-200-2-20000-20000-2-2-2-20000000022-20000-2-2002200000000000000
χ102222222222222222222-2-2222222222-2-200-2-20000-20000-2-2-2-200000000-2-2200002200-2-200000000000000
χ112222222-12-1-1-12-1-1-1-12-12222-1-1-1-1-1-1-12222-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-12220022-1-100-1-1-1-1-1-10000000000
χ122222222-12-1-1-12-1-1-1-12-12222-1-1-1-1-1-1-12222-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-200-2-211001111110000000000
χ132222222-12-1-1-12-1-1-1-12-12222-1-1-1-1-1-1-122-2-2-1-111112-2-2-2-2-1-1-1-11111111122200-2-2-1-100-1-111110000000000
χ142222222-12-1-1-12-1-1-1-12-12222-1-1-1-1-1-1-122-2-2-1-111112-2-2-2-2-1-1-1-111111111-2-2-20022110011-1-1-1-10000000000
χ152222222-12-1-1-12-1-1-1-12-1-2-222-1-1-1-1-1-1-1-2-20011−i3−i3i3i3-200001111−i3−i3−i3−i3i3i3i3i322-200001100-1-1−i3−i3i3i30000000000
χ162222222-12-1-1-12-1-1-1-12-1-2-222-1-1-1-1-1-1-1-2-20011−i3−i3i3i3-200001111−i3−i3−i3−i3i3i3i3i3-2-220000-1-10011i3i3−i3−i30000000000
χ172222222-12-1-1-12-1-1-1-12-1-2-222-1-1-1-1-1-1-1-2-20011i3i3−i3−i3-200001111i3i3i3i3−i3−i3−i3−i322-200001100-1-1i3i3−i3−i30000000000
χ182222222-12-1-1-12-1-1-1-12-1-2-222-1-1-1-1-1-1-1-2-20011i3i3−i3−i3-200001111i3i3i3i3−i3−i3−i3−i3-2-220000-1-10011−i3−i3i3i30000000000
χ19222222-12-1222-12222-1-122-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100022000022000000-1-1-1-1-1-10000
χ20222222-12-1222-12222-1-122-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000-2-20000-2-20000001111110000
χ21222222-12-1222-12222-1-122-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-2-11111-1-1-1-111111111000220000-2-20000001111-1-10000
χ22222222-12-1222-12222-1-122-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-2-11111-1-1-1-111111111000-2-2000022000000-1-1-1-1110000
χ232222-2-22222-2-2222-2-2222-2-2-222-2-2-2-2222002-20000-2000022-2-2000000000002-200000000000000002-20000
χ242222-2-22222-2-2222-2-2222-2-2-222-2-2-2-2222002-20000-2000022-2-200000000000-220000000000000000-220000
χ252222-2-22222-2-2222-2-222-22-2-222-2-2-2-22-2-200-22000020000-2-22200000000000000000000000000000002-200
χ262222-2-22222-2-2222-2-222-22-2-222-2-2-2-22-2-200-22000020000-2-2220000000000000000000000000000000-2200
χ272222-2-2-12-12-2-2-122-2-2-1-12-211-1-11111-1-1-1002-200001−i3−i3i3i3-1-111−i3−i3i3i3−i3−i3i3i30002-2000000000000−i3−i3i3i3-110000
χ282222-2-2-12-12-2-2-122-2-2-1-12-211-1-11111-1-1-1002-200001−i3−i3i3i3-1-111−i3−i3i3i3−i3−i3i3i3000-22000000000000i3i3−i3−i31-10000
χ292222-2-2-12-12-2-2-122-2-2-1-12-211-1-11111-1-1-1002-200001i3i3−i3−i3-1-111i3i3−i3−i3i3i3−i3−i30002-2000000000000i3i3−i3−i3-110000
χ302222-2-2-12-12-2-2-122-2-2-1-12-211-1-11111-1-1-1002-200001i3i3−i3−i3-1-111i3i3−i3−i3i3i3−i3−i3000-22000000000000−i3−i3i3i31-10000
χ312-2-22-222222-2-2-2-2-222-22002-22-222-2-2-20000000000000000000000000002i−2i00000002−22i−2i00002−22−20000−i2i2
χ322-2-22-222222-2-2-2-2-222-22002-22-222-2-2-20000000000000000000000000002i−2i0000000−222i−2i0000−22−220000i2−i2
χ332-2-22-222222-2-2-2-2-222-22002-22-222-2-2-2000000000000000000000000000−2i2i00000002−2−2i2i00002−22−20000i2−i2
χ342-2-22-222222-2-2-2-2-222-22002-22-222-2-2-2000000000000000000000000000−2i2i0000000−22−2i2i0000−22−220000−i2i2
χ35444444-24-2444-24444-2-2-4-4-2-2-2-2-2-2-2-2-22200-4-4000020000222200000000000000000000000000000000000
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
χ37444444-2-2-2-2-2-2-2-2-2-2-2-2144-2-21111111-2-2-4-4-2-22222-222221111-1-1-1-1-1-1-1-1000000000000000000000000000
χ38444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-2-21111111220022−2i3−2i32i32i320000-1-1-1-1i3i3i3i3−i3−i3−i3−i3000000000000000000000000000
χ39444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-2-211111112200222i32i3−2i3−2i320000-1-1-1-1−i3−i3−i3−i3i3i3i3i3000000000000000000000000000
χ404444-4-44-24-2224-2-2224-24-4-4-4-2-22222-24400-220000-40000-2-22200000000000000000000000000000000000
χ414444-4-44-24-2224-2-2224-2-44-4-4-2-22222-2-4-4002-200004000022-2-200000000000000000000000000000000000
χ424444-4-4-24-24-4-4-244-4-4-2-2-4422-2-22222-22200-440000-2000022-2-200000000000000000000000000000000000
χ434444-4-4-2-2-2-222-2-2-222-214-42211-1-1-1-11-2-200-2200002−2i3−2i32i32i311-1-1i3i3−i3−i3i3i3−i3−i3000000000000000000000000000
χ444444-4-4-2-2-2-222-2-2-222-214-42211-1-1-1-11-2-200-22000022i32i3−2i3−2i311-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000000000000
χ454444-4-4-2-2-2-222-2-2-222-21-442211-1-1-1-1122002-20000-20000-1-11133-3-3-3-333000000000000000000000000000
χ464444-4-4-2-2-2-222-2-2-222-21-442211-1-1-1-1122002-20000-20000-1-111-3-33333-3-3000000000000000000000000000
χ4744-4-40044-4-40044-400-440000-440000-4000000000000000000000000000000002i−2i0000002i−2i2i−2i0000000000
χ4844-4-40044-4-40044-400-440000-440000-400000000000000000000000000000000−2i2i000000−2i2i−2i2i0000000000
χ4944-4-4004-2-42−2i32i34-22−2i32i3-4-200002-2−2i32i3−2i32i32000000000000000000000000000000002i−2i0000002ζ14−2ζ142ζ22−2ζ220000000000
χ5044-4-4004-2-42−2i32i34-22−2i32i3-4-200002-2−2i32i3−2i32i3200000000000000000000000000000000−2i2i000000−2ζ142ζ14−2ζ222ζ220000000000
χ5144-4-4004-2-422i3−2i34-222i3−2i3-4-200002-22i3−2i32i3−2i32000000000000000000000000000000002i−2i0000002ζ22−2ζ222ζ14−2ζ140000000000
χ5244-4-4004-2-422i3−2i34-222i3−2i3-4-200002-22i3−2i32i3−2i3200000000000000000000000000000000−2i2i000000−2ζ222ζ22−2ζ142ζ140000000000
χ534-44-40044-4-400-4-4400440000-4-400004002-2002-22-202-22-200002-22-22-22-2000000000000000000000000000
χ544-44-40044-4-400-4-4400440000-4-40000400-2200-22-220-22-220000-22-22-22-22000000000000000000000000000
χ554-44-4004-2-42−2i32i3-42-22i3−2i34-20000222i3−2i3−2i32i3-2002-200−1−i31+i3−1+i31−i302-22-20000−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i3000000000000000000000000000
χ564-44-4004-2-42−2i32i3-42-22i3−2i34-20000222i3−2i3−2i32i3-200-22001+i3−1−i31−i3−1+i30-22-2200001+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i3000000000000000000000000000
χ574-44-4004-2-422i3−2i3-42-2−2i32i34-2000022−2i32i32i3−2i3-2002-200−1+i31−i3−1−i31+i302-22-20000−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i3000000000000000000000000000
χ584-44-4004-2-422i3−2i3-42-2−2i32i34-2000022−2i32i32i3−2i3-200-22001−i3−1+i31+i3−1−i30-22-2200001−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i3000000000000000000000000000
χ594-44-400-242-4002-4400-2-20000220000-2−2i32i32-2002-22-20−1−i31+i3−1+i31−i3−2i32i300−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3000000000000000000000000000
χ604-44-400-242-4002-4400-2-20000220000-2−2i32i3-2200-22-2201+i3−1−i31−i3−1+i3−2i32i3001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3000000000000000000000000000
χ614-44-400-242-4002-4400-2-20000220000-22i3−2i32-2002-22-20−1+i31−i3−1−i31+i32i3−2i300−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3000000000000000000000000000
χ624-44-400-242-4002-4400-2-20000220000-22i3−2i3-2200-22-2201−i3−1+i31+i3−1−i32i3−2i3001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3000000000000000000000000000
χ634-44-400-2-222−2i32i322-22i3−2i3-210000-1-1−i3i3i3−i31−2i32i32-200−1−i31+i3−1+i31−i30−1−i31+i3−1+i31−i3i3−i33-32+i3−2−i3-11-112−i3−2+i3000000000000000000000000000
χ644-44-400-2-222−2i32i322-22i3−2i3-210000-1-1−i3i3i3−i31−2i32i3-22001+i3−1−i31−i3−1+i301+i3−1−i31−i3−1+i3i3−i33-3−2−i32+i31-11-1−2+i32−i3000000000000000000000000000
χ654-44-400-2-222−2i32i322-22i3−2i3-210000-1-1−i3i3i3−i312i3−2i32-200−1−i31+i3−1+i31−i30−1+i31−i3−1−i31+i3−i3i3-33-112+i3−2−i32−i3−2+i3-11000000000000000000000000000
χ664-44-400-2-222−2i32i322-22i3−2i3-210000-1-1−i3i3i3−i312i3−2i3-22001+i3−1−i31−i3−1+i301−i3−1+i31+i3−1−i3−i3i3-331-1−2−i32+i3−2+i32−i31-1000000000000000000000000000
χ674-44-400-2-2222i3−2i322-2−2i32i3-210000-1-1i3−i3−i3i31−2i32i32-200−1+i31−i3−1−i31+i30−1−i31+i3−1+i31−i3i3−i3-33-112−i3−2+i32+i3−2−i3-11000000000000000000000000000
χ684-44-400-2-2222i3−2i322-2−2i32i3-210000-1-1i3−i3−i3i31−2i32i3-22001−i3−1+i31+i3−1−i301+i3−1−i31−i3−1+i3i3−i3-331-1−2+i32−i3−2−i32+i31-1000000000000000000000000000
χ694-44-400-2-2222i3−2i322-2−2i32i3-210000-1-1i3−i3−i3i312i3−2i32-200−1+i31−i3−1−i31+i30−1+i31−i3−1−i31+i3−i3i33-32−i3−2+i3-11-112+i3−2−i3000000000000000000000000000
χ704-44-400-2-2222i3−2i322-2−2i32i3-210000-1-1i3−i3−i3i312i3−2i3-22001−i3−1+i31+i3−1−i301−i3−1+i31+i3−1−i3−i3i33-3−2+i32−i31-11-1−2−i32+i3000000000000000000000000000
χ714-4-444-4444444-4-4-4-4-4-4400-444-4-4-444-4000000000000000000000000000000000000000000000000000000
χ724-4-444-44-24-2-2-2-42222-4-200-44-2222-2-220000000000000000000000000000000000−2i32i3000000000000000000
χ734-4-444-44-24-2-2-2-42222-4-200-44-2222-2-2200000000000000000000000000000000002i3−2i3000000000000000000
χ744-4-444-4-24-24442-4-4-4-42-2002-2-2222-2-2200000000000000000000000000000000000000000000i6−i6−i6i6000000
χ754-4-444-4-24-24442-4-4-4-42-2002-2-2222-2-2200000000000000000000000000000000000000000000−i6i6i6−i6000000
χ764-4-44-444-24-222-422-2-2-4-2004-4-22-2-22220000000000000000000000000004i−4i000000000−2i2i00000000000000
χ774-4-44-444-24-222-422-2-2-4-2004-4-22-2-2222000000000000000000000000000−4i4i0000000002i−2i00000000000000
χ784-4-44-44-24-24-4-42-4-4442-200-22-22-2-222200000000000000000000000000000000000022−22000000−22−22000000
χ794-4-44-44-24-24-4-42-4-4442-200-22-22-2-2222000000000000000000000000000000000000−22220000002−22−2000000
χ8088-8-800-484-800-48-8004-400004-400004000000000000000000000000000000000000000000000000000000
χ8188-8-800-4-444−4i34i3-4-44−4i34i3420000-222i3−2i32i3−2i3-2000000000000000000000000000000000000000000000000000000
χ8288-8-800-4-4444i3−4i3-4-444i3−4i3420000-22−2i32i3−2i32i3-2000000000000000000000000000000000000000000000000000000
χ838-8-888-8-4-4-4-4-4-44444442004-42-2-2-222-2000000000000000000000000000000000000000000000000000000
χ848-8-88-88-4-4-4-444444-4-44200-442-222-2-2-2000000000000000000000000000000000000000000000000000000

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