Finite Group Databasebeta

← Group #11778142

Character table — Group #11778142

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222224444444444444444448888888888888888888888824242424242424242424242424242424242424242424242472727272
order12222233666666666634444666666666121212124121212121212121212121212121212121212121212122244666688881212121224242424242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1111111111111111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11-11-1
χ61111111111111111111-1-1111111111111111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-11-11
χ71111111111111111111-1-1111111111111111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-11-11
χ81111111111111111111-1-1111111111111111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-11-1
χ9222222222222222222222-2-2222222222-2-2-2-2-22222-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ102222222222222222222-2-2-2-2222222222-2-2-2-22-2-2-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ112222222-12-1-1-12-12-1-1-1-1222222-1-1-1-1-1-1-12222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-10000-1-1-1-1000000000000
χ122222222-12-1-1-12-12-1-1-1-1222222-1-1-1-1-1-1-12222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111100001111000000000000
χ132222222-12-1-1-12-12-1-1-1-122-2-222-1-1-1-1-1-1-1-2-2-2-2-222-1-111-2-211-1-1-1-1111111110000−i3−i3i3i30000−i3−i3i3i3000000000000
χ142222222-12-1-1-12-12-1-1-1-122-2-222-1-1-1-1-1-1-1-2-2-2-2-222-1-111-2-211-1-1-1-1111111110000i3i3−i3−i30000i3i3−i3−i3000000000000
χ152222222-12-1-1-12-12-1-1-1-1-2-22222-1-1-1-1-1-1-12222-2-2-211-1-1-2-2111111-1-1-1-1111122-2-2-1-1-1-100001111000000000000
χ162222222-12-1-1-12-12-1-1-1-1-2-22222-1-1-1-1-1-1-12222-2-2-211-1-1-2-2111111-1-1-1-11111-2-22211110000-1-1-1-1000000000000
χ172222222-12-1-1-12-12-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-22-2-2111122-1-111111111-1-1-1-10000−i3−i3i3i30000i3i3−i3−i3000000000000
χ182222222-12-1-1-12-12-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-22-2-2111122-1-111111111-1-1-1-10000i3i3−i3−i30000−i3−i3i3i3000000000000
χ19222222-12-1222-12-1222-12222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12222-1-122-1-1-1-1-1-1-1-1-1-1-1-10000000022220000-1-1-1-1-1-1-1-10000
χ20222222-12-1222-12-1222-12222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12222-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-20000111111110000
χ21222222-12-1222-12-1222-122-2-2-1-1-1-1-1-1-1-1-11111-2-1-122-2-211-2-2-1-1-1-111111111000000000000000033−3−333−3−30000
χ22222222-12-1222-12-1222-122-2-2-1-1-1-1-1-1-1-1-11111-2-1-122-2-211-2-2-1-1-1-1111111110000000000000000−3−333−3−3330000
χ23222222-12-1222-12-1222-1-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-211-2-22211-2-21111-1-1-1-111110000000022-2-20000-1-1-1-111110000
χ24222222-12-1222-12-1222-1-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-211-2-22211-2-21111-1-1-1-1111100000000-2-22200001111-1-1-1-10000
χ25222222-12-1222-12-1222-1-2-2-2-2-1-1-1-1-1-1-1-1-11111211-2-2-2-2-1-12211111111-1-1-1-1000000000000000033−3−3−3−3330000
χ26222222-12-1222-12-1222-1-2-2-2-2-1-1-1-1-1-1-1-1-11111211-2-2-2-2-1-12211111111-1-1-1-10000000000000000−3−33333−3−30000
χ272222-2-22222-2-22222-2-22002-2-2-22-2-2-2-22222-2-2000002-20000000022-2-2000000000000000000000000000020-20
χ282222-2-22222-2-22222-2-22002-2-2-22-2-2-2-22222-2-2000002-20000000022-2-20000000000000000000000000000-2020
χ292222-2-22222-2-22222-2-2200-22-2-22-2-2-2-222-2-22200000-2200000000-2-2220000000000000000000000000000020-2
χ302222-2-22222-2-22222-2-2200-22-2-22-2-2-2-222-2-22200000-2200000000-2-22200000000000000000000000000000-202
χ3122-2-2-2222-2-2-2-222-2-22222-2002-2-222-2-22-2000002-22-200000022-2-20000000000000000−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i20000
χ3222-2-2-2222-2-2-2-222-2-22222-2002-2-222-2-22-2000002-22-200000022-2-20000000000000000i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i20000
χ3322-2-2-2222-2-2-2-222-2-2222-22002-2-222-2-22-200000-22-22000000-2-2220000000000000000−i2i2i2−i20000−i2i2−i2i2i2−i2i2−i20000
χ3422-2-2-2222-2-2-2-222-2-2222-22002-2-222-2-22-200000-22-22000000-2-2220000000000000000i2−i2−i2i20000i2−i2i2−i2−i2i2−i2i20000
χ3522-2-2-22-121-2-2-2-121-222-12-200-111-1-111-113−33−30-112-2003−300-1-1113−33−333−3−300000000−i2i2−i2i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ3622-2-2-22-121-2-2-2-121-222-12-200-111-1-111-113−33−30-112-2003−300-1-1113−33−333−3−300000000i2−i2i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ3722-2-2-22-121-2-2-2-121-222-12-200-111-1-111-11−33−330-112-200−3300-1-111−33−33−3−33300000000−i2i2−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ3822-2-2-22-121-2-2-2-121-222-12-200-111-1-111-11−33−330-112-200−3300-1-111−33−33−3−33300000000i2−i2i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ3922-2-2-22-121-2-2-2-121-222-1-2200-111-1-111-113−33−301-1-2200−330011-1-13−33−3−3−33300000000−i2i2i2−i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ4022-2-2-22-121-2-2-2-121-222-1-2200-111-1-111-113−33−301-1-2200−330011-1-13−33−3−3−33300000000i2−i2−i2i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ4122-2-2-22-121-2-2-2-121-222-1-2200-111-1-111-11−33−3301-1-22003−30011-1-1−33−3333−3−300000000−i2i2i2−i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ4222-2-2-22-121-2-2-2-121-222-1-2200-111-1-111-11−33−3301-1-22003−30011-1-1−33−3333−3−300000000i2−i2−i2i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ43444444-2-2-2-2-2-2-2-2-2-2-2-214444-2-21111111-2-2-2-24-2-2-2-2-2-2-2-2-2-21111111111110000000000000000000000000000
χ44444444-2-2-2-2-2-2-2-2-2-2-2-2144-4-4-2-211111112222-4-2-2-2-22222221111-1-1-1-1-1-1-1-10000000000000000000000000000
χ45444444-2-2-2-2-2-2-2-2-2-2-2-21-4-444-2-21111111-2-2-2-2-42222-2-22222-1-1-1-11111-1-1-1-10000000000000000000000000000
χ46444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-4-4-2-2111111122224222222-2-2-2-2-1-1-1-1-1-1-1-111110000000000000000000000000000
χ474444-4-44-24-2224-24-222-2004-4-4-4-22222-2-244-4-400000-2200000000-2-22200000000000000000000000000000000
χ484444-4-44-24-2224-24-222-200-44-4-4-22222-2-2-4-444000002-20000000022-2-200000000000000000000000000000000
χ494444-4-4-24-24-4-4-24-24-4-4-2004-422-22222-2-2-2-222000004-400000000-2-22200000000000000000000000000000000
χ504444-4-4-24-24-4-4-24-24-4-4-200-4422-22222-2-222-2-200000-440000000022-2-200000000000000000000000000000000
χ514444-4-4-2-2-2-222-2-2-2-2221004-4221-1-1-1-111-2-22200000-2200003-33-311-1-13-33-30000000000000000000000000000
χ524444-4-4-2-2-2-222-2-2-2-2221004-4221-1-1-1-111-2-22200000-220000-33-3311-1-1-33-330000000000000000000000000000
χ534444-4-4-2-2-2-222-2-2-2-222100-44221-1-1-1-11122-2-2000002-200003-33-3-1-111-33-330000000000000000000000000000
χ544444-4-4-2-2-2-222-2-2-2-222100-44221-1-1-1-11122-2-2000002-20000-33-33-1-1113-33-30000000000000000000000000000
χ5544-4-44-444-4-44444-4-4-4-440000-44-4-4-4444-40000000000000000000000000000000000000000000000000000000
χ5644-4-44-44-2-42-2-24-2-4222-20000-44222-2-2-22000000000000023−230000000023−23−23230000000000000000000000000000
χ5744-4-44-44-2-42-2-24-2-4222-20000-44222-2-2-220000000000000−232300000000−232323−230000000000000000000000000000
χ5844-4-44-4-242-444-242-4-4-4-200002-2222-2-2-2223−23−232300000000000000023−23−232300000000000000000000000000000000
χ5944-4-44-4-242-444-242-4-4-4-200002-2222-2-2-22−232323−23000000000000000−232323−2300000000000000000000000000000000
χ6044-4-44-4-2-222-2-2-2-22222100002-2-1-1-1111-123−23−232300000000023−23-333-3−333−3−333−30000000000000000000000000000
χ6144-4-44-4-2-222-2-2-2-22222100002-2-1-1-1111-123−23−2323000000000−23233-3-33−333−33−3−330000000000000000000000000000
χ6244-4-44-4-2-222-2-2-2-22222100002-2-1-1-1111-1−232323−2300000000023−233-3-333−3−33−333−30000000000000000000000000000
χ6344-4-44-4-2-222-2-2-2-22222100002-2-1-1-1111-1−232323−23000000000−2323-333-33−3−333−3−330000000000000000000000000000
χ6444-4-4-444-2-42224-2-42-2-2-24-4004-42-2-222-22000004-4-22000000-2-222000000000000000000000000000000000000
χ6544-4-4-444-2-42224-2-42-2-2-2-44004-42-2-222-2200000-442-200000022-2-2000000000000000000000000000000000000
χ6644-4-4-44-2-22222-2-222-2-214-400-22-111-1-11-123−2323−230-22-220023−230011-1-1−33−33−3−3330000000000000000000000000000
χ6744-4-4-44-2-22222-2-222-2-214-400-22-111-1-11-1−2323−23230-22-2200−23230011-1-13−33−333−3−30000000000000000000000000000
χ6844-4-4-44-2-22222-2-222-2-21-4400-22-111-1-11-123−2323−2302-22-200−232300-1-111−33−3333−3−30000000000000000000000000000
χ6944-4-4-44-2-22222-2-222-2-21-4400-22-111-1-11-1−2323−232302-22-20023−2300-1-1113−33−3−3−3330000000000000000000000000000
χ704-44-400444400-4-4-4-400400000040000-4-4000000000000000000000000000002i−2i000000002i−2i2i−2i000000000000
χ714-44-400444400-4-4-4-400400000040000-4-400000000000000000000000000000−2i2i00000000−2i2i−2i2i000000000000
χ724-44-4004-24-2−2i32i3-42-42−2i32i3-2000000-2−2i32i3−2i32i322000000000000000000000000000002i−2i000000002ζ14−2ζ142ζ22−2ζ22000000000000
χ734-44-4004-24-2−2i32i3-42-42−2i32i3-2000000-2−2i32i3−2i32i32200000000000000000000000000000−2i2i00000000−2ζ142ζ14−2ζ222ζ22000000000000
χ744-44-4004-24-22i3−2i3-42-422i3−2i3-2000000-22i3−2i32i3−2i322000000000000000000000000000002i−2i000000002ζ22−2ζ222ζ14−2ζ14000000000000
χ754-44-4004-24-22i3−2i3-42-422i3−2i3-2000000-22i3−2i32i3−2i32200000000000000000000000000000−2i2i00000000−2ζ222ζ22−2ζ142ζ14000000000000
χ764-4-440044-4-400-4-444004000000-40000-440000000000000000000000000002-2002-22-200000000000000000000
χ774-4-440044-4-400-4-444004000000-40000-44000000000000000000000000000-2200-22-2200000000000000000000
χ784-4-44004-2-42−2i32i3-424-22i3−2i3-200000022i3−2i3−2i32i32-20000000000000000000000000002-200−1−i31+i3−1+i31−i300000000000000000000
χ794-4-44004-2-42−2i32i3-424-22i3−2i3-200000022i3−2i3−2i32i32-2000000000000000000000000000-22001+i3−1−i31−i3−1+i300000000000000000000
χ804-4-44004-2-422i3−2i3-424-2−2i32i3-20000002−2i32i32i3−2i32-20000000000000000000000000002-200−1+i31−i3−1−i31+i300000000000000000000
χ814-4-44004-2-422i3−2i3-424-2−2i32i3-20000002−2i32i32i3−2i32-2000000000000000000000000000-22001−i3−1+i31+i3−1−i300000000000000000000
χ828-88-800-48-48004-84-800-4000000-40000440000000000000000000000000000000000000000000000000000000
χ838-88-800-4-4-4-4−4i34i34444−4i34i3200000022i3−2i32i3−2i3-2-20000000000000000000000000000000000000000000000000000000
χ848-88-800-4-4-4-44i3−4i344444i3−4i320000002−2i32i3−2i32i3-2-20000000000000000000000000000000000000000000000000000000
χ858-8-8800-484-8004-8-4800-4000000400004-40000000000000000000000000000000000000000000000000000000
χ868-8-8800-4-444−4i34i344-4-44i3−4i32000000-2−2i32i32i3−2i3-220000000000000000000000000000000000000000000000000000000
χ878-8-8800-4-4444i3−4i344-4-4−4i34i32000000-22i3−2i3−2i32i3-220000000000000000000000000000000000000000000000000000000

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