Finite Group Databasebeta

← Group #11778708

Character table — Group #11778708

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222224444444444444444448888888888888888888888824242424242424242424242424242424242424242424242472727272
order1222223366666666662234466666666612121212466666666121212121212121212121212121244448888121212121212121224242424242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
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
χ5111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11-11-1
χ6111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-11-11
χ7111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-11-11
χ8111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111-11-1
χ9222222222222222222222-2-2222222222-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ10222222222222222222-2-22-2-2222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ112222222-1222-12-1-122222-122-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-10000
χ122222222-1222-12-1-122222-122-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000-2-2-2-200000000111111110000
χ132222222-1222-12-1-122222-1-2-2-1-1-1-1-1-1-1-1-11111-222-1-1-1-1-1-1-2-211-2-211111111000000000000000033−3−333−3−30000
χ142222222-1222-12-1-122222-1-2-2-1-1-1-1-1-1-1-1-11111-222-1-1-1-1-1-1-2-211-2-2111111110000000000000000−3−333−3−3330000
χ152222222-1222-12-1-1222-2-2-122-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-21111112211-2-2-1-1-1-11111000022-2-200000000-1-1-1-111110000
χ162222222-1222-12-1-1222-2-2-122-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-21111112211-2-2-1-1-1-111110000-2-222000000001111-1-1-1-10000
χ172222222-1222-12-1-1222-2-2-1-2-2-1-1-1-1-1-1-1-1-111112-2-2111111-2-2-1-1221111-1-1-1-1000000000000000033−3−3−3−3330000
χ182222222-1222-12-1-1222-2-2-1-2-2-1-1-1-1-1-1-1-1-111112-2-2111111-2-2-1-1221111-1-1-1-10000000000000000−3−33333−3−30000
χ19222222-12-1-1-12-122-1-1-122-12222-1-1-1-1-1-1-122222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-1000000000000
χ20222222-12-1-1-12-122-1-1-122-12222-1-1-1-1-1-1-122222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2000011111111000000000000
χ21222222-12-1-1-12-122-1-1-122-1-2-222-1-1-1-1-1-1-1-2-2-2-2-2-1-122-1-1-1-111-2-2111111111100000000−i3−i3i3i3−i3−i3i3i3000000000000
χ22222222-12-1-1-12-122-1-1-122-1-2-222-1-1-1-1-1-1-1-2-2-2-2-2-1-122-1-1-1-111-2-2111111111100000000i3i3−i3−i3i3i3−i3−i3000000000000
χ23222222-12-1-1-12-122-1-1-1-2-2-12222-1-1-1-1-1-1-12222-211-2-21111-1-1-2-211-1-1-1-1111122-2-200001111-1-1-1-1000000000000
χ24222222-12-1-1-12-122-1-1-1-2-2-12222-1-1-1-1-1-1-12222-211-2-21111-1-1-2-211-1-1-1-11111-2-2220000-1-1-1-11111000000000000
χ25222222-12-1-1-12-122-1-1-1-2-2-1-2-222-1-1-1-1-1-1-1-2-2-2-2211-2-211111122-1-11111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3000000000000
χ26222222-12-1-1-12-122-1-1-1-2-2-1-2-222-1-1-1-1-1-1-1-2-2-2-2211-2-211111122-1-11111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3000000000000
χ272222-2-2222-2-22222-2-220022-2-2-22-2-2-2-22222-2-20000000002-2000022-2-2000000000000000000000000000020-20
χ282222-2-2222-2-22222-2-220022-2-2-22-2-2-2-22222-2-20000000002-2000022-2-20000000000000000000000000000-2020
χ292222-2-2222-2-22222-2-22002-22-2-22-2-2-2-222-2-222000000000-220000-2-2220000000000000000000000000000020-2
χ302222-2-2222-2-22222-2-22002-22-2-22-2-2-2-222-2-222000000000-220000-2-22200000000000000000000000000000-202
χ3122-2-22-2222222-2-2-2-2-2-22-22002-2222-2-2-2-2000002-22-222-2-20000000000000000002−22−2000000002−22−22−22−20000
χ3222-2-22-2222222-2-2-2-2-2-22-22002-2222-2-2-2-2000002-22-222-2-2000000000000000000−22−2200000000−22−22−22−220000
χ3322-2-22-2222222-2-2-2-2-2-2-222002-2222-2-2-2-200000-22-22-2-2220000000000000000002−2−22000000002−22−2−22−220000
χ3422-2-22-2222222-2-2-2-2-2-2-222002-2222-2-2-2-200000-22-22-2-222000000000000000000−222−200000000−22−222−22−20000
χ3522-2-22-22-1222-1-211-2-2-22-2-100-11-1-1-111113−33−302-2-11-1-111003−3003−33−333−3−300002−22−200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000
χ3622-2-22-22-1222-1-211-2-2-22-2-100-11-1-1-111113−33−302-2-11-1-111003−3003−33−333−3−30000−22−2200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000
χ3722-2-22-22-1222-1-211-2-2-22-2-100-11-1-1-11111−33−3302-2-11-1-11100−3300−33−33−3−33300002−22−200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000
χ3822-2-22-22-1222-1-211-2-2-22-2-100-11-1-1-11111−33−3302-2-11-1-11100−3300−33−33−3−3330000−22−2200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000
χ3922-2-22-22-1222-1-211-2-2-2-22-100-11-1-1-111113−33−30-221-111-1-100−33003−33−3−3−33300002−2−2200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000
χ4022-2-22-22-1222-1-211-2-2-2-22-100-11-1-1-111113−33−30-221-111-1-100−33003−33−3−3−3330000−222−200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000
χ4122-2-22-22-1222-1-211-2-2-2-22-100-11-1-1-11111−33−330-221-111-1-1003−300−33−3333−3−300002−2−2200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000
χ4222-2-22-22-1222-1-211-2-2-2-22-100-11-1-1-11111−33−330-221-111-1-1003−300−33−3333−3−30000−222−200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000
χ43444444-2-2-2-2-2-2-2-2-2-2-2-244144-2-21111111-2-2-2-24-2-2-2-21111-2-2-2-2-2-2111111110000000000000000000000000000
χ44444444-2-2-2-2-2-2-2-2-2-2-2-2441-4-4-2-211111112222-4-2-2-2-21111222222-1-1-1-1-1-1-1-10000000000000000000000000000
χ45444444-2-2-2-2-2-2-2-2-2-2-2-2-4-4144-2-21111111-2-2-2-2-42222-1-1-1-1-2-222221111-1-1-1-10000000000000000000000000000
χ46444444-2-2-2-2-2-2-2-2-2-2-2-2-4-41-4-4-2-21111111222242222-1-1-1-122-2-2-2-2-1-1-1-111110000000000000000000000000000
χ474444-4-44-24-4-4-24-2-2-4-4400-24-422-22222-2-2-2-2220000000004-40000-2-22200000000000000000000000000000000
χ484444-4-44-24-4-4-24-2-2-4-4400-2-4422-22222-2-222-2-2000000000-44000022-2-200000000000000000000000000000000
χ494444-4-4-24-2224-24422-200-24-4-4-4-22222-2-244-4-4000000000-220000-2-22200000000000000000000000000000000
χ504444-4-4-24-2224-24422-200-2-44-4-4-22222-2-2-4-4440000000002-2000022-2-200000000000000000000000000000000
χ514444-4-4-2-2-222-2-2-2-222-20014-4221-1-1-1-111-2-222000003-33-3-22000011-1-13-33-30000000000000000000000000000
χ524444-4-4-2-2-222-2-2-2-222-20014-4221-1-1-1-111-2-22200000-33-33-22000011-1-1-33-330000000000000000000000000000
χ534444-4-4-2-2-222-2-2-2-222-2001-44221-1-1-1-11122-2-2000003-33-32-20000-1-111-33-330000000000000000000000000000
χ544444-4-4-2-2-222-2-2-2-222-2001-44221-1-1-1-11122-2-200000-33-332-20000-1-1113-33-30000000000000000000000000000
χ5544-4-44-4-24-2-2-242-4-42224-4-2004-4-2-2-2222200000-224-4-2-222000000000000000000000000000000000000000000
χ5644-4-44-4-24-2-2-242-4-4222-44-2004-4-2-2-22222000002-2-4422-2-2000000000000000000000000000000000000000000
χ5744-4-44-4-2-2-2-2-2-22222224-4100-22111-1-1-1-123−2323−230-22-2211-1-10023−2300−33−33−3−3330000000000000000000000000000
χ5844-4-44-4-2-2-2-2-2-22222224-4100-22111-1-1-1-1−2323−23230-22-2211-1-100−2323003−33−333−3−30000000000000000000000000000
χ5944-4-44-4-2-2-2-2-2-2222222-44100-22111-1-1-1-123−2323−2302-22-2-1-11100−232300−33−3333−3−30000000000000000000000000000
χ6044-4-44-4-2-2-2-2-2-2222222-44100-22111-1-1-1-1−2323−232302-22-2-1-1110023−23003−33−3−3−3330000000000000000000000000000
χ6144-4-4-44444-4-44-4-4-444-400400-444-4-444-4-40000000000000000000000000000000000000000000000000000000
χ6244-4-4-444-24-4-4-2-42244-400-2002-2-222-2-22223−23−232300000000000000023−23−232300000000000000000000000000000000
χ6344-4-4-444-24-4-4-2-42244-400-2002-2-222-2-222−232323−23000000000000000−232323−2300000000000000000000000000000000
χ6444-4-4-44-24-22242-4-4-2-2200-200-44-222-2-2220000000000000000023−23000023−23−23230000000000000000000000000000
χ6544-4-4-44-24-22242-4-4-2-2200-200-44-222-2-22200000000000000000−23230000−232323−230000000000000000000000000000
χ6644-4-4-44-2-2-222-2222-2-22001002-21-1-111-1-123−23−2323000003-3-330000−2323−333−33−3−330000000000000000000000000000
χ6744-4-4-44-2-2-222-2222-2-22001002-21-1-111-1-123−23−232300000-333-3000023−23−333−3−333−30000000000000000000000000000
χ6844-4-4-44-2-2-222-2222-2-22001002-21-1-111-1-1−232323−23000003-3-33000023−233−3−33−333−30000000000000000000000000000
χ6944-4-4-44-2-2-222-2222-2-22001002-21-1-111-1-1−232323−2300000-333-30000−23233−3−333−3−330000000000000000000000000000
χ704-44-40044-400-444-400-40040000-400004-40000000000000000000000000002i−2i00000000002i−2i2i−2i000000000000
χ714-44-40044-400-444-400-40040000-400004-4000000000000000000000000000−2i2i0000000000−2i2i−2i2i000000000000
χ724-44-400-242−2i32i3-4-24-4−2i32i3200-200002−2i32i3−2i32i3-220000000000000000000000000002i−2i00000000002ζ22−2ζ222ζ14−2ζ14000000000000
χ734-44-400-242−2i32i3-4-24-4−2i32i3200-200002−2i32i3−2i32i3-22000000000000000000000000000−2i2i0000000000−2ζ222ζ22−2ζ142ζ14000000000000
χ744-44-400-2422i3−2i3-4-24-42i3−2i3200-2000022i3−2i32i3−2i3-220000000000000000000000000002i−2i00000000002ζ14−2ζ142ζ22−2ζ22000000000000
χ754-44-400-2422i3−2i3-4-24-42i3−2i3200-2000022i3−2i32i3−2i3-22000000000000000000000000000−2i2i0000000000−2ζ142ζ14−2ζ222ζ22000000000000
χ764-4-440044-400-4-4-440040040000-40000-44000000000000000000000000000002-200002-22-20000000000000000
χ774-4-440044-400-4-4-440040040000-40000-4400000000000000000000000000000-220000-22-220000000000000000
χ784-4-4400-242−2i32i3-42-442i3−2i3-200-200002−2i32i32i3−2i32-2000000000000000000000000000002-20000−1−i31+i3−1+i31−i30000000000000000
χ794-4-4400-242−2i32i3-42-442i3−2i3-200-200002−2i32i32i3−2i32-200000000000000000000000000000-2200001+i3−1−i31−i3−1+i30000000000000000
χ804-4-4400-2422i3−2i3-42-44−2i32i3-200-2000022i3−2i3−2i32i32-2000000000000000000000000000002-20000−1+i31−i3−1−i31+i30000000000000000
χ814-4-4400-2422i3−2i3-42-44−2i32i3-200-2000022i3−2i3−2i32i32-200000000000000000000000000000-2200001−i3−1+i31+i3−1−i30000000000000000
χ828-88-8008-4-80048-4400-800-4000040000-440000000000000000000000000000000000000000000000000000000
χ838-88-800-4-44−4i34i34-4-44−4i34i340020000-22i3−2i32i3−2i32-20000000000000000000000000000000000000000000000000000000
χ848-88-800-4-444i3−4i34-4-444i3−4i340020000-2−2i32i3−2i32i32-20000000000000000000000000000000000000000000000000000000
χ858-8-88008-4-8004-84-400800-40000400004-40000000000000000000000000000000000000000000000000000000
χ868-8-8800-4-44−4i34i3444-44i3−4i3-40020000-22i3−2i3−2i32i3-220000000000000000000000000000000000000000000000000000000
χ878-8-8800-4-444i3−4i3444-4−4i34i3-40020000-2−2i32i32i3−2i3-220000000000000000000000000000000000000000000000000000000

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