Finite Group Databasebeta

← Group #11778789

Character table — Group #11778789

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222224444444444444444448888888888888888888888824242424242424242424242424242424242424242424242472727272
order12222233666666666634444666666666121212124121212121212121212121212121212121212121212122244444466661212121212121212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ51111111111111111111-1-111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-1111-1-1-111-1-1-1-1-1-1111111-1-111-1-1
χ61111111111111111111-1-111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-11-11111-1-11111-1-1-1-111-1-1-1-111
χ71111111111111111111-1-111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1111-11-1-1-1-111-1-1-1-11111-1-111-1-111
χ81111111111111111111-1-111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-1111-1-1111111-1-1-1-1-1-11111-1-1
χ9222222222222222222222-2-22222222222222-222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ102222222222222222222-2-2-2-2222222222-2-2-2-22-2-2-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ112222222-122-122-1222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-122222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-122002200-1-1-1-100000000-1-1-1-10000
χ122222222-122-122-1222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-122222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-20011110000000011110000
χ132222222-122-122-1222-1-122-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-222-2-211-2-211-1-1-1-11111111100000000−i3i3−i3i300000000−i3i3−i3i30000
χ142222222-122-122-1222-1-122-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-222-2-211-2-211-1-1-1-11111111100000000i3−i3i3−i300000000i3−i3i3−i30000
χ152222222-122-122-1222-1-1-2-222-1-1-1-1-1-1-1-1-11111-2-2-222-1-1-2-2111111-1-1-1-111112-2002-200-1-11100000000-1-1110000
χ162222222-122-122-1222-1-1-2-222-1-1-1-1-1-1-1-1-11111-2-2-222-1-1-2-2111111-1-1-1-11111-2200-220011-1-10000000011-1-10000
χ172222222-122-122-1222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-111112-2-2-2-21122-1-111111111-1-1-1-100000000−i3i3i3−i300000000−i3i3i3−i30000
χ182222222-122-122-1222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-111112-2-2-2-21122-1-111111111-1-1-1-100000000i3−i3−i3i300000000i3−i3−i3i30000
χ19222222-12-1-12-1-12-1-1-12-1222222-1-1-1-1-1-1-122222-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1002200220000-1-1-1-1-1-1-1-100000000
χ20222222-12-1-12-1-12-1-1-12-1222222-1-1-1-1-1-1-122222-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-100-2-200-2-200001111111100000000
χ21222222-12-1-12-1-12-1-1-12-122-2-222-1-1-1-1-1-1-12222-2-1-111-2-211-2-2-1-1-1-111111111000000000000−i3−i3i3i3−i3−i3i3i300000000
χ22222222-12-1-12-1-12-1-1-12-122-2-222-1-1-1-1-1-1-12222-2-1-111-2-211-2-2-1-1-1-111111111000000000000i3i3−i3−i3i3i3−i3−i300000000
χ23222222-12-1-12-1-12-1-1-12-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-211-1-12211-2-21111-1-1-1-11111002200-2-200001111-1-1-1-100000000
χ24222222-12-1-12-1-12-1-1-12-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-211-1-12211-2-21111-1-1-1-1111100-2-200220000-1-1-1-1111100000000
χ25222222-12-1-12-1-12-1-1-12-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-221111-2-2-1-12211111111-1-1-1-1000000000000−i3−i3i3i3i3i3−i3−i300000000
χ26222222-12-1-12-1-12-1-1-12-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-221111-2-2-1-12211111111-1-1-1-1000000000000i3i3−i3−i3−i3−i3i3i300000000
χ272222-2-222-2-22222-2-2222002-2-2-22-2-2-2-22200000002-22-20000000022-2-2000002000-20000220000000000-2-20000
χ282222-2-222-2-22222-2-2222002-2-2-22-2-2-2-22200000002-22-20000000022-2-200000-200020000-2-20000000000220000
χ292222-2-222-2-22222-2-222200-22-2-22-2-2-2-2220000000-22-2200000000-2-22200002000-2000220000000000-2-2000000
χ302222-2-222-2-22222-2-222200-22-2-22-2-2-2-2220000000-22-2200000000-2-2220000-20002000-2-2000000000022000000
χ312222-2-22-1-2-2-122-1-2-22-1-1002-211-11111-1-1−i3−i3i3i30002-2-1100−i3i3−i3−i3i3i3-1-111−i3−i3i3i302000-200−i3i3-1-100000000i3−i3110000
χ322222-2-22-1-2-2-122-1-2-22-1-1002-211-11111-1-1−i3−i3i3i30002-2-1100−i3i3−i3−i3i3i3-1-111−i3−i3i3i30-2000200i3−i31100000000−i3i3-1-10000
χ332222-2-22-1-2-2-122-1-2-22-1-1002-211-11111-1-1i3i3−i3−i30002-2-1100i3−i3i3i3−i3−i3-1-111i3i3−i3−i302000-200i3−i3-1-100000000−i3i3110000
χ342222-2-22-1-2-2-122-1-2-22-1-1002-211-11111-1-1i3i3−i3−i30002-2-1100i3−i3i3i3−i3−i3-1-111i3i3−i3−i30-2000200−i3i31100000000i3−i3-1-10000
χ352222-2-22-1-2-2-122-1-2-22-1-100-2211-11111-1-1−i3−i3i3i3000-221-100i3−i3−i3−i3i3i311-1-1i3i3−i3−i32000-2000-1-1−i3i30000000011i3−i30000
χ362222-2-22-1-2-2-122-1-2-22-1-100-2211-11111-1-1−i3−i3i3i3000-221-100i3−i3−i3−i3i3i311-1-1i3i3−i3−i3-2000200011i3−i300000000-1-1−i3i30000
χ372222-2-22-1-2-2-122-1-2-22-1-100-2211-11111-1-1i3i3−i3−i3000-221-100−i3i3i3i3−i3−i311-1-1−i3−i3i3i32000-2000-1-1i3−i30000000011−i3i30000
χ382222-2-22-1-2-2-122-1-2-22-1-100-2211-11111-1-1i3i3−i3−i3000-221-100−i3i3i3i3−i3−i311-1-1−i3−i3i3i3-2000200011−i3i300000000-1-1i3−i30000
χ392-2-222-22222-22-2-2-2-2-2222-2002-2-222-2-22-22-22-202-2000000002-22-200000000000000000000000000000000−i2i2−i2i2
χ402-2-222-22222-22-2-2-2-2-2222-2002-2-222-2-22-22-22-202-2000000002-22-200000000000000000000000000000000i2−i2i2−i2
χ412-2-222-22222-22-2-2-2-2-222-22002-2-222-2-22-2-22-220-2200000000-22-2200000000000000000000000000000000−i2i2i2−i2
χ422-2-222-22222-22-2-2-2-2-222-22002-2-222-2-22-2-22-220-2200000000-22-2200000000000000000000000000000000i2−i2−i2i2
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
χ44444444-2-2-2-2-2-2-2-2-2-2-2-2144-4-4-2-21111111-2-2-2-2-4-2-2222222221111-1-1-1-1-1-1-1-10000000000000000000000000000
χ45444444-2-2-2-2-2-2-2-2-2-2-2-21-4-444-2-211111112222-422-2-2-2-22222-1-1-1-11111-1-1-1-10000000000000000000000000000
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
χ474444-4-4-24224-2-2422-24-2004-4-4-4-22222-2-20000000-224-400000000-2-22200000000000000000000000000000000
χ484444-4-4-24224-2-2422-24-200-44-4-4-22222-2-200000002-2-440000000022-2-200000000000000000000000000000000
χ494444-4-4-2-222-2-2-2-222-2-21004-4221-1-1-1-111−2i3−2i32i32i3000-22-2200−2i32i3i3i3−i3−i311-1-1i3i3−i3−i30000000000000000000000000000
χ504444-4-4-2-222-2-2-2-222-2-21004-4221-1-1-1-1112i32i3−2i3−2i3000-22-22002i3−2i3−i3−i3i3i311-1-1−i3−i3i3i30000000000000000000000000000
χ514444-4-4-2-222-2-2-2-222-2-2100-44221-1-1-1-111−2i3−2i32i32i30002-22-2002i3−2i3i3i3−i3−i3-1-111−i3−i3i3i30000000000000000000000000000
χ524444-4-4-2-222-2-2-2-222-2-2100-44221-1-1-1-1112i32i3−2i3−2i30002-22-200−2i32i3−i3−i3i3i3-1-111i3i3−i3−i30000000000000000000000000000
χ5344-4-4004400-4-44400-4-44000000-40000-44000000000000000000000000000002i−2i0000000000002i−2i2i−2i00000000
χ5444-4-4004400-4-44400-4-44000000-40000-4400000000000000000000000000000−2i2i000000000000−2i2i−2i2i00000000
χ5544-4-400-24−2i32i3-42-24−2i32i32-4-20000002−2i32i3−2i32i32-2000000000000000000000000000002i−2i0000000000002ζ14−2ζ142ζ22−2ζ2200000000
χ5644-4-400-24−2i32i3-42-24−2i32i32-4-20000002−2i32i3−2i32i32-200000000000000000000000000000−2i2i000000000000−2ζ142ζ14−2ζ222ζ2200000000
χ5744-4-400-242i3−2i3-42-242i3−2i32-4-200000022i3−2i32i3−2i32-2000000000000000000000000000002i−2i0000000000002ζ22−2ζ222ζ14−2ζ1400000000
χ5844-4-400-242i3−2i3-42-242i3−2i32-4-200000022i3−2i32i3−2i32-200000000000000000000000000000−2i2i000000000000−2ζ222ζ22−2ζ142ζ1400000000
χ594-44-40044004-4-4-4004-4400000040000-4-40000000000000000000000000000000002i−2i00002i−2i2i−2i000000000000
χ604-44-40044004-4-4-4004-4400000040000-4-4000000000000000000000000000000000−2i2i0000−2i2i−2i2i000000000000
χ614-44-400-24−2i32i3422-42i3−2i3-2-4-2000000-2−2i32i32i3−2i3220000000000000000000000000000000002i−2i00002ζ14−2ζ142ζ22−2ζ22000000000000
χ624-44-400-24−2i32i3422-42i3−2i3-2-4-2000000-2−2i32i32i3−2i322000000000000000000000000000000000−2i2i0000−2ζ142ζ14−2ζ222ζ22000000000000
χ634-44-400-242i3−2i3422-4−2i32i3-2-4-2000000-22i3−2i3−2i32i3220000000000000000000000000000000002i−2i00002ζ22−2ζ222ζ14−2ζ14000000000000
χ644-44-400-242i3−2i3422-4−2i32i3-2-4-2000000-22i3−2i3−2i32i322000000000000000000000000000000000−2i2i0000−2ζ222ζ22−2ζ142ζ14000000000000
χ654-4-444-44-24424-42-4-4-4-2-24-400-222-2-222-22-22-2204-400000000-22-22000000000000000000000000000000000000
χ664-4-444-44-24424-42-4-4-4-2-2-4400-222-2-222-222-22-20-44000000002-22-2000000000000000000000000000000000000
χ674-4-444-4-24-2-2-4-22-42224-24-4004-42-2-222-224-44-40-2200000000-22-22000000000000000000000000000000000000
χ684-4-444-4-24-2-2-4-22-42224-2-44004-42-2-222-22-44-4402-2000000002-22-2000000000000000000000000000000000000
χ694-4-444-4-2-2-2-22-222222-214-400-22-111-1-11-1-22-220-22000000001-11-13i−3i3i−3i3i−3i3i−3i0000000000000000000000000000
χ704-4-444-4-2-2-2-22-222222-214-400-22-111-1-11-1-22-220-22000000001-11-1−3i3i−3i3i−3i3i−3i3i0000000000000000000000000000
χ714-4-444-4-2-2-2-22-222222-21-4400-22-111-1-11-12-22-202-200000000-11-113i−3i3i−3i−3i3i−3i3i0000000000000000000000000000
χ724-4-444-4-2-2-2-22-222222-21-4400-22-111-1-11-12-22-202-200000000-11-11−3i3i−3i3i3i−3i3i−3i0000000000000000000000000000
χ734-4-44-4444-4-4-44-4-444-4440000-44-4-4-4444-40000000000000000000000000000000000000000000000000000000
χ744-4-44-444-2-4-424-4244-4-2-200002-2222-2-2-22−2i32i32i3−2i300000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ754-4-44-444-2-4-424-4244-4-2-200002-2222-2-2-222i3−2i3−2i32i3000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ764-4-44-44-2422-4-22-4-2-224-20000-44222-2-2-220000000000023−23000000000023−23−23230000000000000000000000000000
χ774-4-44-44-2422-4-22-4-2-224-20000-44222-2-2-2200000000000−23230000000000−232323−230000000000000000000000000000
χ784-4-44-44-2-2222-222-2-22-2100002-2-1-1-1111-1−2i32i32i3−2i3000000023−2300i3−i3−i3i3−3i3i3i−3i−333−30000000000000000000000000000
χ794-4-44-44-2-2222-222-2-22-2100002-2-1-1-1111-1−2i32i32i3−2i30000000−232300i3−i3−i3i33i−3i−3i3i3−3−330000000000000000000000000000
χ804-4-44-44-2-2222-222-2-22-2100002-2-1-1-1111-12i3−2i3−2i32i3000000023−2300−i3i3i3−i33i−3i−3i3i−333−30000000000000000000000000000
χ814-4-44-44-2-2222-222-2-22-2100002-2-1-1-1111-12i3−2i3−2i32i30000000−232300−i3i3i3−i3−3i3i3i−3i3−3−330000000000000000000000000000
χ8288-8-8008-4004-88-400-84-4000000400004-40000000000000000000000000000000000000000000000000000000
χ8388-8-800-4-4−4i34i344-4-4−4i34i3442000000-22i3−2i32i3−2i3-220000000000000000000000000000000000000000000000000000000
χ8488-8-800-4-44i3−4i344-4-44i3−4i3442000000-2−2i32i3−2i32i3-220000000000000000000000000000000000000000000000000000000
χ858-88-8008-400-4-8-840084-4000000-40000440000000000000000000000000000000000000000000000000000000
χ868-88-800-4-4−4i34i3-44444i3−4i3-44200000022i3−2i3−2i32i3-2-20000000000000000000000000000000000000000000000000000000
χ878-88-800-4-44i3−4i3-4444−4i34i3-4420000002−2i32i32i3−2i3-2-20000000000000000000000000000000000000000000000000000000

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