Finite Group Databasebeta

← Group #11778064

Character table — Group #11778064

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444448888888888888888888888888121224242424242424242424242424242424242424484872727272
order1222223366666666663446666666661212226666666666666666121212121212124424444881212121212121212242424246124488
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
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-11111-1-1-1-1111111-1-1-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1111-1-1-1-11111-1-1-1-1-1-111-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-11111-1-11111-1-11111-1-111-1-1
χ92222222222222222222-2-2222222222-2-2000000000000000000-2-2-2-2-2-2-2220-200000-2-20000220000000000
χ102222222222222222222-2-2222222222-2-2000000000000000000-2-2-2-2-2-2-2-2-20200000220000-2-20000000000
χ112222222-1222-1-1222-12-122-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100202002200000000-1-1-1-1-1-10000
χ122222222-1222-1-1222-12-122-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100-20-200-2-2000000001111110000
χ132222222-1222-1-1222-12-122-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111111111-122-1-1-1-10020200-2-2000000001111-1-10000
χ142222222-1222-1-1222-12-122-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111111111-122-1-1-1-100-20-2002200000000-1-1-1-1110000
χ15222222-12-1-1-122-1-1-12-1-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-1-1-1220202200-1-1-1-1-1-1-1-10000000000
χ16222222-12-1-1-122-1-1-12-1-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-1-1-1-2-20-20-2-200111111110000000000
χ17222222-12-1-1-122-1-1-12-1-12222-1-1-1-1-1-1-122-2-21111-2-2-2-2111111112-1-1-1-1-1-122020-2-200-1-11111-1-10000000000
χ18222222-12-1-1-122-1-1-12-1-12222-1-1-1-1-1-1-122-2-21111-2-2-2-2111111112-1-1-1-1-1-1-2-20-20220011-1-1-1-1110000000000
χ19222222-12-1-1-122-1-1-12-1-1-2-222-1-1-1-1-1-1-1-2-200−i3−i3i3i30000−i3−i3−i3−i3i3i3i3i3-2111111220-20000011−i3−i3i3i3-1-10000000000
χ20222222-12-1-1-122-1-1-12-1-1-2-222-1-1-1-1-1-1-1-2-200−i3−i3i3i30000−i3−i3−i3−i3i3i3i3i3-2111111-2-20200000-1-1i3i3−i3−i3110000000000
χ21222222-12-1-1-122-1-1-12-1-1-2-222-1-1-1-1-1-1-1-2-200i3i3−i3−i30000i3i3i3i3−i3−i3−i3−i3-2111111220-20000011i3i3−i3−i3-1-10000000000
χ22222222-12-1-1-122-1-1-12-1-1-2-222-1-1-1-1-1-1-1-2-200i3i3−i3−i30000i3i3i3i3−i3−i3−i3−i3-2111111-2-20200000-1-1−i3−i3i3i3110000000000
χ232222-2-2222-2-2222-2-22222-2-2-222-2-2-2-2222000000000000000000-22-222-2-20020-200000000000000002-20000
χ242222-2-2222-2-2222-2-22222-2-2-222-2-2-2-2222000000000000000000-22-222-2-200-2020000000000000000-220000
χ252222-2-2222-2-2222-2-2222-22-2-222-2-2-2-22-2-20000000000000000002-22-2-222000000000000000000000002-200
χ262222-2-2222-2-2222-2-2222-22-2-222-2-2-2-22-2-20000000000000000002-22-2-22200000000000000000000000-2200
χ272222-2-22-12-2-2-1-12-2-2-12-12-211-1-11111-1-1-1000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i312-2-1-1110020-2000000000000−i3−i3i3i3-110000
χ282222-2-22-12-2-2-1-12-2-2-12-12-211-1-11111-1-1-1000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i312-2-1-11100-202000000000000i3i3−i3−i31-10000
χ292222-2-22-12-2-2-1-12-2-2-12-12-211-1-11111-1-1-1000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i312-2-1-1110020-2000000000000i3i3−i3−i3-110000
χ302222-2-22-12-2-2-1-12-2-2-12-12-211-1-11111-1-1-1000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i312-2-1-11100-202000000000000−i3−i3i3i31-10000
χ3122-2-22-222-222-2-22-2-22-22002-22-222-2-2-20000000000000000000000000002i−2i000002−20000002i−2i2−22−20000−i2i2
χ3222-2-22-222-222-2-22-2-22-22002-22-222-2-2-20000000000000000000000000002i−2i00000−220000002i−2i−22−220000i2−i2
χ3322-2-22-222-222-2-22-2-22-22002-22-222-2-2-2000000000000000000000000000−2i2i000002−2000000−2i2i2−22−20000i2−i2
χ3422-2-22-222-222-2-22-2-22-22002-22-222-2-2-2000000000000000000000000000−2i2i00000−22000000−2i2i−22−220000−i2i2
χ354444444-2444-2-2444-24-2-4-4-2-2-2-2-2-2-2-2-2220000000000000000002-4-42222000000000000000000000000000
χ36444444-2-2-2-2-2-2-2-2-2-2-2-2144-2-21111111-2-244-2-2-2-2-2-2-2-211111111-2-2-21111000000000000000000000000000
χ37444444-2-2-2-2-2-2-2-2-2-2-2-2144-2-21111111-2-2-4-422222222-1-1-1-1-1-1-1-1-2-2-21111000000000000000000000000000
χ38444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-2-211111112200−2i3−2i32i32i30000i3i3i3i3−i3−i3−i3−i3222-1-1-1-1000000000000000000000000000
χ39444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-2-2111111122002i32i3−2i3−2i30000−i3−i3−i3−i3i3i3i3i3222-1-1-1-1000000000000000000000000000
χ404444-4-44-24-4-4-2-24-4-4-24-2-4422-2-22222-222000000000000000000-2-4422-2-2000000000000000000000000000
χ414444-4-4-24-22244-2224-2-24-4-4-4-2-22222-244000000000000000000-4-22-2-222000000000000000000000000000
χ424444-4-4-24-22244-2224-2-2-44-4-4-2-22222-2-4-400000000000000000042-222-2-2000000000000000000000000000
χ434444-4-4-2-2-222-2-2-222-2-214-42211-1-1-1-11-2-2000000−2i3−2i32i32i3i3i3−i3−i3i3i3−i3−i32-2211-1-1000000000000000000000000000
χ444444-4-4-2-2-222-2-2-222-2-214-42211-1-1-1-11-2-20000002i32i3−2i3−2i3−i3−i3i3i3−i3−i3i3i32-2211-1-1000000000000000000000000000
χ454444-4-4-2-2-222-2-2-222-2-21-442211-1-1-1-1122000000000033-3-3-3-333-22-2-1-111000000000000000000000000000
χ464444-4-4-2-2-222-2-2-222-2-21-442211-1-1-1-11220000000000-3-33333-3-3-22-2-1-111000000000000000000000000000
χ4744-4-44-44-2-444224-4-4-2-4-200-22-22-2-2222000000000000000000000000000000000022−2200000000−22−22000000
χ4844-4-44-44-2-444224-4-4-2-4-200-22-22-2-22220000000000000000000000000000000000−2222000000002−22−2000000
χ4944-4-44-4-242-2-2-4-4-22242-2004-4-22-2-22220000000000000000000000000004i−4i0000000000000−2i2i0000000000
χ5044-4-44-4-242-2-2-4-4-22242-2004-4-22-2-2222000000000000000000000000000−4i4i00000000000002i−2i0000000000
χ5144-4-4-4444-4-4-4-4-44444-4400-444-4-4-444-4000000000000000000000000000000000000000000000000000000
χ5244-4-4-444-2-4-4-422444-2-4-2002-2-2222-2-2200000000000000000000000000000000000000000000i6−i6−i6i6000000
χ5344-4-4-444-2-4-4-422444-2-4-2002-2-2222-2-2200000000000000000000000000000000000000000000−i6i6i6−i6000000
χ5444-4-4-44-24222-4-4-2-2-242-200-44-2222-2-22000000000000000000000000000000000000−2i32i30000000000000000
χ5544-4-4-44-24222-4-4-2-2-242-200-44-2222-2-220000000000000000000000000000000000002i3−2i30000000000000000
χ564-44-400444004-4-400-4-440000-440000-4000000000000000000000000000000002i−2i00002i−2i2i−2i000000000000
χ574-44-400444004-4-400-4-440000-440000-400000000000000000000000000000000−2i2i0000−2i2i−2i2i000000000000
χ584-44-400-24-2−2i32i34-42−2i32i3-42-200002-2−2i32i3−2i32i32000000000000000000000000000000002i−2i00002ζ14−2ζ142ζ22−2ζ22000000000000
χ594-44-400-24-2−2i32i34-42−2i32i3-42-200002-2−2i32i3−2i32i3200000000000000000000000000000000−2i2i0000−2ζ142ζ14−2ζ222ζ22000000000000
χ604-44-400-24-22i3−2i34-422i3−2i3-42-200002-22i3−2i32i3−2i32000000000000000000000000000000002i−2i00002ζ22−2ζ222ζ14−2ζ14000000000000
χ614-44-400-24-22i3−2i34-422i3−2i3-42-200002-22i3−2i32i3−2i3200000000000000000000000000000000−2i2i0000−2ζ222ζ22−2ζ142ζ14000000000000
χ624-4-440044-400-44-400-4440000-4-400004002-22-22-22-22-22-22-22-22-20000000000000000000000000000000000
χ634-4-440044-400-44-400-4440000-4-40000400-22-22-22-22-22-22-22-22-220000000000000000000000000000000000
χ644-4-44004-2-4002-2-40024-20000220000-2−2i32i32-22-22-2−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3000−2i32i300000000000000000000000000000
χ654-4-44004-2-4002-2-40024-20000220000-2−2i32i3-22-22-221+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3000−2i32i300000000000000000000000000000
χ664-4-44004-2-4002-2-40024-20000220000-22i3−2i32-22-22-2−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i30002i3−2i300000000000000000000000000000
χ674-4-44004-2-4002-2-40024-20000220000-22i3−2i3-22-22-221−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i30002i3−2i300000000000000000000000000000
χ684-4-4400-242−2i32i3-4422i3−2i3-4-2-2000022−2i32i32i3−2i3-2002-2−1+i31−i3−1−i31+i32-22-2−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i30000000000000000000000000000000000
χ694-4-4400-242−2i32i3-4422i3−2i3-4-2-2000022−2i32i32i3−2i3-200-221−i3−1+i31+i3−1−i3-22-221−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i30000000000000000000000000000000000
χ704-4-4400-2422i3−2i3-442−2i32i3-4-2-20000222i3−2i3−2i32i3-2002-2−1−i31+i3−1+i31−i32-22-2−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i30000000000000000000000000000000000
χ714-4-4400-2422i3−2i3-442−2i32i3-4-2-20000222i3−2i3−2i32i3-200-221+i3−1−i31−i3−1+i3-22-221+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i30000000000000000000000000000000000
χ724-4-4400-2-22−2i32i32-222i3−2i32-210000-1-1i3−i3−i3i31−2i32i32-2−1+i31−i3−1−i31+i3−1−i31+i3−1+i31−i3-112−i3−2+i32+i3−2−i3-11000i3−i33-3000000000000000000000000000
χ734-4-4400-2-22−2i32i32-222i3−2i32-210000-1-1i3−i3−i3i31−2i32i3-221−i3−1+i31+i3−1−i31+i3−1−i31−i3−1+i31-1−2+i32−i3−2−i32+i31-1000i3−i33-3000000000000000000000000000
χ744-4-4400-2-22−2i32i32-222i3−2i32-210000-1-1i3−i3−i3i312i3−2i32-2−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i32−i3−2+i3-11-112+i3−2−i3000−i3i3-33000000000000000000000000000
χ754-4-4400-2-22−2i32i32-222i3−2i32-210000-1-1i3−i3−i3i312i3−2i3-221−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3−2+i32−i31-11-1−2−i32+i3000−i3i3-33000000000000000000000000000
χ764-4-4400-2-222i3−2i32-22−2i32i32-210000-1-1−i3i3i3−i31−2i32i32-2−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i32+i3−2−i3-11-112−i3−2+i3000i3−i3-33000000000000000000000000000
χ774-4-4400-2-222i3−2i32-22−2i32i32-210000-1-1−i3i3i3−i31−2i32i3-221+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3−2−i32+i31-11-1−2+i32−i3000i3−i3-33000000000000000000000000000
χ784-4-4400-2-222i3−2i32-22−2i32i32-210000-1-1−i3i3i3−i312i3−2i32-2−1−i31+i3−1+i31−i3−1+i31−i3−1−i31+i3-112+i3−2−i32−i3−2+i3-11000−i3i33-3000000000000000000000000000
χ794-4-4400-2-222i3−2i32-22−2i32i32-210000-1-1−i3i3i3−i312i3−2i3-221+i3−1−i31−i3−1+i31−i3−1+i31+i3−1−i31-1−2−i32+i3−2+i32−i31-1000−i3i33-3000000000000000000000000000
χ8088-8-88-8-4-44-4-444-444-44200-442-222-2-2-2000000000000000000000000000000000000000000000000000000
χ8188-8-8-88-4-444444-4-4-4-442004-42-2-2-222-2000000000000000000000000000000000000000000000000000000
χ828-88-8008-4800-44-8004-8-400004-400004000000000000000000000000000000000000000000000000000000
χ838-88-800-4-4-4−4i34i3-444−4i34i34420000-222i3−2i32i3−2i3-2000000000000000000000000000000000000000000000000000000
χ848-88-800-4-4-44i3−4i3-4444i3−4i34420000-22−2i32i3−2i32i3-2000000000000000000000000000000000000000000000000000000

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