Finite Group Databasebeta

← Group #11778741

Character table — Group #11778741

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222244444444444444444488888888888888888888888824242424242424242424242424242424363648484848727272
order1222223366666634466666666666121212124412121212121212121212121212121212121212121212244488882424242424242424446121212444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-11-111-1-11111-1-1-1-1-1-111-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-11-11-1-111-1-1-1-11111-1-1-1-111-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111
χ511111111111111111111111111111111-1-11-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1
χ611111111111111111111111111111111-1-11-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-11111-1-111-1-1-111
χ711111111111111111111111111111111-1-11-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-1-1-1-1-111-111
χ811111111111111111111111111111111-1-11-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11-1-1
χ9222222222222222-2-222222222222-2-2-2-200-20000-20000-2-2-2-2000000000000000000000000220000-200
χ10222222222222222-2-222222222222-2-2-2-200-20000-20000-2-2-2-2000000000000000000000000-2-20000200
χ112222222-12-1-1-122-12222-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-120202200-1-1-1-1000000-1-100000
χ122222222-12-1-1-122-12222-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-20-20-2-20011110000001100000
χ132222222-12-1-1-122-12222-1-1-1-1-1-1-1-1-1-1-122-2-2-111112-2-2-2-2-1-1-1-1111111112020-2-2001111000000-1-100000
χ142222222-12-1-1-122-12222-1-1-1-1-1-1-1-1-1-1-122-2-2-111112-2-2-2-2-1-1-1-111111111-20-202200-1-1-1-10000001100000
χ15222222-12-1222-1-1-122-1-122-1-1-1-1-1-1-122-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1020200220000-1-1-1-10000-1-1000
χ16222222-12-1222-1-1-122-1-122-1-1-1-1-1-1-122-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10-20-200-2-200001111000011000
χ17222222-12-1222-1-1-122-1-122-1-1-1-1-1-1-122-1-1-2-22-2-2-2-2-11111-1-1-1-111111111020200-2-2000011110000-1-1000
χ18222222-12-1222-1-1-122-1-122-1-1-1-1-1-1-122-1-1-2-22-2-2-2-2-11111-1-1-1-1111111110-20-200220000-1-1-1-1000011000
χ192222-2-22222222222-2-2-2-2-22-2-2-2-22222-2-200-200002000022-2-20000000020-20000000000000002-200000
χ202222-2-22222222222-2-2-2-2-22-2-2-2-22222-2-200-200002000022-2-200000000-202000000000000000-2200000
χ212222-2-2222222222-22-2-2-2-22-2-2-2-222-2-2220020000-20000-2-22200000000020-20000000000000000-22000
χ222222-2-2222222222-22-2-2-2-22-2-2-2-222-2-2220020000-20000-2-222000000000-20200000000000000002-2000
χ232222-2-22-12-1-1-122-12-2-2-211-11111-1-1-1-1-2-2001−i3−i3i3i320000-1-111−i3−i3−i3−i3i3i3i3i320-200000−i3−i3i3i3000000-1100000
χ242222-2-22-12-1-1-122-12-2-2-211-11111-1-1-1-1-2-2001−i3−i3i3i320000-1-111−i3−i3−i3−i3i3i3i3i3-20200000i3i3−i3−i30000001-100000
χ252222-2-22-12-1-1-122-12-2-2-211-11111-1-1-1-1-2-2001i3i3−i3−i320000-1-111i3i3i3i3−i3−i3−i3−i320-200000i3i3−i3−i3000000-1100000
χ262222-2-22-12-1-1-122-12-2-2-211-11111-1-1-1-1-2-2001i3i3−i3−i320000-1-111i3i3i3i3−i3−i3−i3−i3-20200000−i3−i3i3i30000001-100000
χ272222-2-2-12-1222-1-1-1-2211-2-2-11111-1-1-2-2-1-100200001−i3−i3i3i311-1-1−i3−i3i3i3−i3−i3i3i3020-200000000−i3−i3i3i300001-1000
χ282222-2-2-12-1222-1-1-1-2211-2-2-11111-1-1-2-2-1-100200001−i3−i3i3i311-1-1−i3−i3i3i3−i3−i3i3i30-20200000000i3i3−i3−i30000-11000
χ292222-2-2-12-1222-1-1-1-2211-2-2-11111-1-1-2-2-1-100200001i3i3−i3−i311-1-1i3i3−i3−i3i3i3−i3−i3020-200000000i3i3−i3−i300001-1000
χ302222-2-2-12-1222-1-1-1-2211-2-2-11111-1-1-2-2-1-100200001i3i3−i3−i311-1-1i3i3−i3−i3i3i3−i3−i30-20200000000−i3−i3i3i30000-11000
χ312-22-2-22222-2-22-2-22002-22-2222-2-2-2-200000000000000000000000000000000−i2i22−2−i2i2−i2i22−22−22i−2i0000000
χ322-22-2-22222-2-22-2-22002-22-2222-2-2-2-200000000000000000000000000000000−i2i2−22−i2i2−i2i2−22−22−2i2i0000000
χ332-22-2-22222-2-22-2-22002-22-2222-2-2-2-200000000000000000000000000000000i2−i22−2i2−i2i2−i22−22−2−2i2i0000000
χ342-22-2-22222-2-22-2-22002-22-2222-2-2-2-200000000000000000000000000000000i2−i2−22i2−i2i2−i2−22−222i−2i0000000
χ354444444-24-2-2-244-2-4-444-2-2-2-2-2-2-2-2-222-4-40020000-400002222000000000000000000000000000000000
χ36444444-24-2444-2-2-2-4-4-2-244-2-2-2-2-2-2-2-4-42200-40000200002222000000000000000000000000000000000
χ37444444-2-2-2-2-2-2-2-2144-2-2-2-21111111-2-2-2-244-2-2-2-2-2-2-2-2-2-21111111111110000000000000000000000000
χ38444444-2-2-2-2-2-2-2-2144-2-2-2-21111111-2-2-2-2-4-4-22222-222221111-1-1-1-1-1-1-1-10000000000000000000000000
χ39444444-2-2-2-2-2-2-2-21-4-4-2-2-2-211111112222002000020000-1-1-1-133-3-3-3-3330000000000000000000000000
χ40444444-2-2-2-2-2-2-2-21-4-4-2-2-2-211111112222002000020000-1-1-1-1-3-33333-3-30000000000000000000000000
χ414444-4-44-24-2-2-244-2-44-4-422-22222-2-2224400-20000-4000022-2-2000000000000000000000000000000000
χ424444-4-4-24-2444-2-2-24-422-4-4-22222-2-2442200-40000-20000-2-222000000000000000000000000000000000
χ434444-4-4-2-2-2-2-2-2-2-214-422221-1-1-1-111-2-222002−2i3−2i32i32i3-2000011-1-1i3i3i3i3−i3−i3−i3−i30000000000000000000000000
χ444444-4-4-2-2-2-2-2-2-2-214-422221-1-1-1-111-2-2220022i32i3−2i3−2i3-2000011-1-1−i3−i3−i3−i3i3i3i3i30000000000000000000000000
χ454444-4-4-2-2-2-2-2-2-2-21-4422221-1-1-1-11122-2-200-200002−2i3−2i32i32i3-1-111i3i3−i3−i3i3i3−i3−i30000000000000000000000000
χ464444-4-4-2-2-2-2-2-2-2-21-4422221-1-1-1-11122-2-200-2000022i32i3−2i3−2i3-1-111−i3−i3i3i3−i3−i3i3i30000000000000000000000000
χ4744-4-40044-4-44-4-444000000-40000-440000000000000000000000000000000000000000000000000002i−2i
χ4844-4-40044-4-44-4-444000000-40000-44000000000000000000000000000000000000000000000000000−2i2i
χ494-44-44-4444-4-44-4-4400-44-444-4-444-4-400000000000000000000000000000000000000000000000000000
χ504-44-44-44-2422-2-4-4-200-442-2-222-2-2220000000000000000000000000000000000006−6−660000000000000
χ514-44-44-44-2422-2-4-4-200-442-2-222-2-222000000000000000000000000000000000000−666−60000000000000
χ524-44-44-4-24-2-4-4422-2002-2-44-222-2-2220000000000000000000000000000000000000000i6−i6−i6i6000000000
χ534-44-44-4-24-2-4-4422-2002-2-44-222-2-2220000000000000000000000000000000000000000−i6i6i6−i6000000000
χ544-44-4-444-2422-2-4-4-2004-4-22-2-2-2222200000000000000000000000000000000−2i22i200i2−i2i2−i20000000000000
χ554-44-4-444-2422-2-4-4-2004-4-22-2-2-22222000000000000000000000000000000002i2−2i200−i2i2−i2i20000000000000
χ564-44-4-44-24-2-4-4422-200-224-4-2-2-22222000000000000000000000000000000000022−220000−22−22000000000
χ574-44-4-44-24-2-4-4422-200-224-4-2-2-222220000000000000000000000000000000000−222200002−22−2000000000
χ584-4-440044-44-4-44-44000000-400004-400002i−2i02i−2i2i−2i02i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i0000000000000000000000000
χ594-4-440044-44-4-44-44000000-400004-40000−2i2i0−2i2i−2i2i0−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000
χ604-4-44004-2-4-2224-4-200000020000-22−2i32i3002i−2i02ζ14−2ζ142ζ22−2ζ2202i−2i2i−2i−2i32i3002ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ220000000000000000000000000
χ614-4-44004-2-4-2224-4-200000020000-22−2i32i300−2i2i0−2ζ142ζ14−2ζ222ζ220−2i2i−2i2i−2i32i300−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ220000000000000000000000000
χ624-4-44004-2-4-2224-4-200000020000-222i3−2i3002i−2i02ζ22−2ζ222ζ14−2ζ1402i−2i2i−2i2i3−2i3002ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ140000000000000000000000000
χ634-4-44004-2-4-2224-4-200000020000-222i3−2i300−2i2i0−2ζ222ζ22−2ζ142ζ140−2i2i−2i2i2i3−2i300−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ140000000000000000000000000
χ644-4-4400-2424-4-4-22-200000020000-2200−2i32i32i−2i02i−2i2i−2i02ζ14−2ζ142ζ22−2ζ2200−2i32i32ζ14−2ζ142ζ22−2ζ222ζ14−2ζ142ζ22−2ζ220000000000000000000000000
χ654-4-4400-2424-4-4-22-200000020000-2200−2i32i3−2i2i0−2i2i−2i2i0−2ζ142ζ14−2ζ222ζ2200−2i32i3−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14−2ζ222ζ220000000000000000000000000
χ664-4-4400-2424-4-4-22-200000020000-22002i3−2i32i−2i02i−2i2i−2i02ζ22−2ζ222ζ14−2ζ14002i3−2i32ζ22−2ζ222ζ14−2ζ142ζ22−2ζ222ζ14−2ζ140000000000000000000000000
χ674-4-4400-2424-4-4-22-200000020000-22002i3−2i3−2i2i0−2i2i−2i2i0−2ζ222ζ22−2ζ142ζ14002i3−2i3−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22−2ζ142ζ140000000000000000000000000
χ684-4-4400-2-22-222-221000000-13-33-31-1−2i32i3−2i32i32i−2i02ζ14−2ζ142ζ22−2ζ2202ζ14−2ζ142ζ22−2ζ22i3−i3i3−i3−3ζ14−ζ223ζ14+ζ22−ii−ii−ζ14−3ζ22ζ14+3ζ220000000000000000000000000
χ694-4-4400-2-22-222-221000000-13-33-31-1−2i32i3−2i32i3−2i2i0−2ζ142ζ14−2ζ222ζ220−2ζ142ζ14−2ζ222ζ22i3−i3i3−i33ζ14+ζ22−3ζ14−ζ22i−ii−iζ14+3ζ22−ζ14−3ζ220000000000000000000000000
χ704-4-4400-2-22-222-221000000-13-33-31-12i3−2i32i3−2i32i−2i02ζ22−2ζ222ζ14−2ζ1402ζ22−2ζ222ζ14−2ζ14−i3i3−i3i3−ζ14−3ζ22ζ14+3ζ22−ii−ii−3ζ14−ζ223ζ14+ζ220000000000000000000000000
χ714-4-4400-2-22-222-221000000-13-33-31-12i3−2i32i3−2i3−2i2i0−2ζ222ζ22−2ζ142ζ140−2ζ222ζ22−2ζ142ζ14−i3i3−i3i3ζ14+3ζ22−ζ14−3ζ22i−ii−i3ζ14+ζ22−3ζ14−ζ220000000000000000000000000
χ724-4-4400-2-22-222-221000000-1-33-331-1−2i32i32i3−2i32i−2i02ζ14−2ζ142ζ22−2ζ2202ζ22−2ζ222ζ14−2ζ14i3−i3−i3i3−ii−3ζ14−ζ223ζ14+ζ22−ζ14−3ζ22ζ14+3ζ22−ii0000000000000000000000000
χ734-4-4400-2-22-222-221000000-1-33-331-1−2i32i32i3−2i3−2i2i0−2ζ142ζ14−2ζ222ζ220−2ζ222ζ22−2ζ142ζ14i3−i3−i3i3i−i3ζ14+ζ22−3ζ14−ζ22ζ14+3ζ22−ζ14−3ζ22i−i0000000000000000000000000
χ744-4-4400-2-22-222-221000000-1-33-331-12i3−2i3−2i32i32i−2i02ζ22−2ζ222ζ14−2ζ1402ζ14−2ζ142ζ22−2ζ22−i3i3i3−i3−ii−ζ14−3ζ22ζ14+3ζ22−3ζ14−ζ223ζ14+ζ22−ii0000000000000000000000000
χ754-4-4400-2-22-222-221000000-1-33-331-12i3−2i3−2i32i3−2i2i0−2ζ222ζ22−2ζ142ζ140−2ζ142ζ14−2ζ222ζ22−i3i3i3−i3i−iζ14+3ζ22−ζ14−3ζ223ζ14+ζ22−3ζ14−ζ22i−i0000000000000000000000000
χ7688-8-8008-4-84-44-88-4000000400004-400000000000000000000000000000000000000000000000000000
χ7788-8-800-484-88-84-4-4000000400004-400000000000000000000000000000000000000000000000000000
χ7888-8-800-4-444-444-42000000-26-6-66-2200000000000000000000000000000000000000000000000000000
χ7988-8-800-4-444-444-42000000-2-666-6-2200000000000000000000000000000000000000000000000000000
χ808-88-88-8-4-4-444-4442004-44-42-2-222-2-200000000000000000000000000000000000000000000000000000
χ818-88-8-88-4-4-444-444200-44-44222-2-2-2-200000000000000000000000000000000000000000000000000000

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