Finite Group Databasebeta

← Group #13155052

Character table — Group #13155052

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112224444444444444444444488888888888888882424242424242424242424242424242424243636363672727272727272216216
order1223623333666666666666666366666666666666644121212121212121212121212121212122444266612121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-11-1-11-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-1-11-1-111
χ511111-11111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1111-1-1-1-1i−iiiiiiiii−i−i−i−i−i−i−i−i-1111-1-1-1-1111i−i
χ611111-11111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1111-1-1-1-1i−iiiiiiiii−i−i−i−i−i−i−i−i-11-1-11-1111-1-1−ii
χ711111-11111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1111-1-1-1-1−ii−i−i−i−i−i−i−i−iiiiiiiii-1111-1-1-1-1111−ii
χ811111-11111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1111-1-1-1-1−ii−i−i−i−i−i−i−i−iiiiiiiii-11-1-11-1111-1-1i−i
χ922222222222222222222222222222222222222222000000000000000000-2-2000-200-20000
χ1022222-22222222222-2-2-2-2-2-2-2-222222-2-2-2-2-2222-2-2-2-20000000000000000002-2000200-20000
χ11222-1-122-1-12-12-1-122-1-122-1-1-1-12-12-1-12-1-122-1-1-1-1-1-1-10000−i3−i3−i3i3i3i300−i3−i3−i3i3i3i3-2-200010010000
χ12222-1-122-1-12-12-1-122-1-122-1-1-1-12-12-1-12-1-122-1-1-1-1-1-1-10000i3i3i3−i3−i3−i300i3i3i3−i3−i3−i3-2-200010010000
χ13222-1-122-1-12-12-1-122-1-122-1-1-1-12-12-1-12-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-122000-100-10000
χ14222-1-122-1-12-12-1-122-1-122-1-1-1-12-12-1-12-1-122-1-1-1-1-1-1-1-2-2-2-2111111-2-211111122000-100-10000
χ15222-1-1-22-1-12-12-1-12211-2-211112-12-1-1-211-2-2-1-1-111110000333−3−3−300−3−3−33332-2000-10010000
χ16222-1-1-22-1-12-12-1-12211-2-211112-12-1-1-211-2-2-1-1-111110000−3−3−333300333−3−3−32-2000-10010000
χ17222-1-1-22-1-12-12-1-12211-2-211112-12-1-1-211-2-2-1-1-111112i−2i2i2i−i−i−i−i−i−i−2i−2iiiiiii-22000100-10000
χ18222-1-1-22-1-12-12-1-12211-2-211112-12-1-1-211-2-2-1-1-11111−2i2i−2i−2iiiiiii2i2i−i−i−i−i−i−i-22000100-10000
χ19444444111-24111-2-244111111-2-2111111-2-2-2-2-2-2-2-2-222-1-12-1-12-1-1-1-12-1-12-1-10000000000000
χ20444444111-24111-2-244111111-2-2111111-2-2-2-2-2-2-2-2-2-2-211-211-21111-211-2110000000000000
χ21444444-2-2-214-2-2-21144-2-2-2-2-2-211-2-2-2-2-2-2111111111000000000000000000002220-1-10-1-100
χ22444444-2-2-214-2-2-21144-2-2-2-2-2-211-2-2-2-2-2-211111111100000000000000000000-2-2-201101100
χ2344444-4111-24111-2-2-4-4-1-1-1-1-1-1-2-2111-1-1-122-2-2-222222i−2i−i−i2i−i−i2i−i−iii−2iii−2iii0000000000000
χ2444444-4111-24111-2-2-4-4-1-1-1-1-1-1-2-2111-1-1-122-2-2-22222−2i2iii−2iii−2iii−i−i2i−i−i2i−i−i0000000000000
χ2544444-4-2-2-214-2-2-211-4-422222211-2-2-2222-1-1111-1-1-1-10000000000000000000022-20110-1-100
χ2644444-4-2-2-214-2-2-211-4-422222211-2-2-2222-1-1111-1-1-1-100000000000000000000-2-220-1-101100
χ27444-2-241−1−3i32−1+3i32-2-21−1−3i32−1+3i32-2-2-2-211−1−3i32−1−3i32−1+3i32−1+3i32-211−1−3i32−1+3i321−1−3i32−1+3i32-2-2111111122-1-1−1−i31+i321+i32−1+i31−i321−i32-1-1−1−i31+i321+i32−1+i31−i321−i320000000000000
χ28444-2-241−1−3i32−1+3i32-2-21−1−3i32−1+3i32-2-2-2-211−1−3i32−1−3i32−1+3i32−1+3i32-211−1−3i32−1+3i321−1−3i32−1+3i32-2-21111111-2-2111+i3−1−i32−1−i321−i3−1+i32−1+i32111+i3−1−i32−1−i321−i3−1+i32−1+i320000000000000
χ29444-2-241−1+3i32−1−3i32-2-21−1+3i32−1−3i32-2-2-2-211−1+3i32−1+3i32−1−3i32−1−3i32-211−1+3i32−1−3i321−1+3i32−1−3i32-2-2111111122-1-1−1+i31−i321−i32−1−i31+i321+i32-1-1−1+i31−i321−i32−1−i31+i321+i320000000000000
χ30444-2-241−1+3i32−1−3i32-2-21−1+3i32−1−3i32-2-2-2-211−1+3i32−1+3i32−1−3i32−1−3i32-211−1+3i32−1−3i321−1+3i32−1−3i32-2-21111111-2-2111−i3−1+i32−1+i321+i3−1−i32−1−i32111−i3−1+i32−1+i321+i3−1−i32−1−i320000000000000
χ31444-2-2-41−1−3i32−1+3i32-2-21−1−3i32−1+3i32-2-222-1-11+3i321+3i321−3i321−3i32-211−1−3i32−1+3i32-11+3i321−3i3222111-1-1-1-12i−2i−i−i2ζ11−ζ11−ζ112ζ7−ζ7−ζ7ii−2ζ11ζ11ζ11−2ζ7ζ7ζ70000000000000
χ32444-2-2-41−1−3i32−1+3i32-2-21−1−3i32−1+3i32-2-222-1-11+3i321+3i321−3i321−3i32-211−1−3i32−1+3i32-11+3i321−3i3222111-1-1-1-1−2i2iii−2ζ11ζ11ζ11−2ζ7ζ7ζ7−i−i2ζ11−ζ11−ζ112ζ7−ζ7−ζ70000000000000
χ33444-2-2-41−1+3i32−1−3i32-2-21−1+3i32−1−3i32-2-222-1-11−3i321−3i321+3i321+3i32-211−1+3i32−1−3i32-11−3i321+3i3222111-1-1-1-12i−2i−i−i2ζ7−ζ7−ζ72ζ11−ζ11−ζ11ii−2ζ7ζ7ζ7−2ζ11ζ11ζ110000000000000
χ34444-2-2-41−1+3i32−1−3i32-2-21−1+3i32−1−3i32-2-222-1-11−3i321−3i321+3i321+3i32-211−1+3i32−1−3i32-11−3i321+3i3222111-1-1-1-1−2i2iii−2ζ7ζ7ζ7−2ζ11ζ11ζ11−i−i2ζ7−ζ7−ζ72ζ11−ζ11−ζ110000000000000
χ3544-4440111-2-41112-2003333332-2-1-1-1-3-3-30022-20000003−303−303−33−303−303−30000000000000
χ3644-4440111-2-41112-2003333332-2-1-1-1-3-3-30022-2000000−330−330−33−330−330−330000000000000
χ3744-4440111-2-41112-200-3-3-3-3-3-32-2-1-1-13330022-2000000−i3i30−i3i30−i3i3i3−i30i3−i30i3−i30000000000000
χ3844-4440111-2-41112-200-3-3-3-3-3-32-2-1-1-13330022-2000000i3−i30i3−i30i3−i3−i3i30−i3i30−i3i30000000000000
χ3944-44404444-4444-4400000000-44-4-4-400000-4-4400000000000000000000000000000000000
χ4044-4-2-201−1−3i32−1+3i32-221−1−3i32−1+3i322-2−2i32i333−3−i32−3−i32−3+i32−3+i3221-11+3i321−3i32-33+i323−i3200-1-11−i3−i3i3i3003−302ζ7+ζ11−2ζ7−ζ110−ζ7−2ζ11ζ7+2ζ113−302ζ7+ζ11−2ζ7−ζ110−ζ7−2ζ11ζ7+2ζ110000000000000
χ4144-4-2-201−1−3i32−1+3i32-221−1−3i32−1+3i322-2−2i32i333−3−i32−3−i32−3+i32−3+i3221-11+3i321−3i32-33+i323−i3200-1-11−i3−i3i3i300−330−2ζ7−ζ112ζ7+ζ110ζ7+2ζ11−ζ7−2ζ11−330−2ζ7−ζ112ζ7+ζ110ζ7+2ζ11−ζ7−2ζ110000000000000
χ4244-4-2-201−1−3i32−1+3i32-221−1−3i32−1+3i322-22i3−2i3-3-33+i323+i323−i323−i3221-11+3i321−3i323−3−i32−3+i3200-1-11i3i3−i3−i300−i3i30−3+i323−i3203+i32−3−i32i3−i303−i32−3+i320−3−i323+i320000000000000
χ4344-4-2-201−1−3i32−1+3i32-221−1−3i32−1+3i322-22i3−2i3-3-33+i323+i323−i323−i3221-11+3i321−3i323−3−i32−3+i3200-1-11i3i3−i3−i300i3−i303−i32−3+i320−3−i323+i32−i3i30−3+i323−i3203+i32−3−i320000000000000
χ4444-4-2-201−1+3i32−1−3i32-221−1+3i32−1−3i322-2−2i32i3-3-33−i323−i323+i323+i3221-11−3i321+3i323−3+i32−3−i3200-1-11−i3−i3i3i300−i3i303+i32−3−i320−3+i323−i32i3−i30−3−i323+i3203−i32−3+i320000000000000
χ4544-4-2-201−1+3i32−1−3i32-221−1+3i32−1−3i322-2−2i32i3-3-33−i323−i323+i323+i3221-11−3i321+3i323−3+i32−3−i3200-1-11−i3−i3i3i300i3−i30−3−i323+i3203−i32−3+i32−i3i303+i32−3−i320−3+i323−i320000000000000
χ4644-4-2-201−1+3i32−1−3i32-221−1+3i32−1−3i322-22i3−2i333−3+i32−3+i32−3−i32−3−i3221-11−3i321+3i32-33−i323+i3200-1-11i3i3−i3−i3003−30−ζ7−2ζ11ζ7+2ζ1102ζ7+ζ11−2ζ7−ζ113−30−ζ7−2ζ11ζ7+2ζ1102ζ7+ζ11−2ζ7−ζ110000000000000
χ4744-4-2-201−1+3i32−1−3i32-221−1+3i32−1−3i322-22i3−2i333−3+i32−3+i32−3−i32−3−i3221-11−3i321+3i32-33−i323+i3200-1-11i3i3−i3−i300−330ζ7+2ζ11−ζ7−2ζ110−2ζ7−ζ112ζ7+ζ11−330ζ7+2ζ11−ζ7−2ζ110−2ζ7−ζ112ζ7+ζ110000000000000
χ4844-4-2-204-2-2424-2-2-44−2i32i300−2i3−2i32i32i3-4-2-42202i3−2i30022-22i32i3−2i3−2i30000000000000000000000000000000
χ4944-4-2-204-2-2424-2-2-442i3−2i3002i32i3−2i3−2i3-4-2-4220−2i32i30022-2−2i3−2i32i32i30000000000000000000000000000000
χ504-404-4044440-4-4-40-400000000040000000000-40000000000000000000000002-2000002-200
χ514-404-4044440-4-4-40-400000000040000000000-4000000000000000000000000-2200000-2200
χ524-404-40-2-2-2102223-100−2i32i3−2i32i3−2i32i3-31000000−i3i33-3-1−i3i3−i3i3000000000000000000002-200−i3i30-1100
χ534-404-40-2-2-2102223-100−2i32i3−2i32i3−2i32i3-31000000−i3i33-3-1−i3i3−i3i300000000000000000000-2200i3−i301-100
χ544-404-40-2-2-2102223-1002i3−2i32i3−2i32i3−2i3-31000000i3−i33-3-1i3−i3i3−i3000000000000000000002-200i3−i30-1100
χ554-404-40-2-2-2102223-1002i3−2i32i3−2i32i3−2i3-31000000i3−i33-3-1i3−i3i3−i300000000000000000000-2200−i3i301-100
χ56888-4-48-4222-4-42222-4-4-4-422222-1-422-42222-1-1-1-1-1-1-10000000000000000000000000000000
χ57888-4-4-8-4222-4-422224444-2-2-2-22-1-4224-2-2-2-2-1-1-111110000000000000000000000000000000
χ5888-8880-4-4-42-8-4-4-4-2200000000-2244400000-2-2200000000000000000000000000000000000
χ5988-8-4-40-42224-422-22−4i34i3002i32i3−2i3−2i3-2-14-2-20−2i32i30011-1i3i3−i3−i30000000000000000000000000000000
χ6088-8-4-40-42224-422-224i3−4i300−2i3−2i32i32i3-2-14-2-202i3−2i30011-1−i3−i3i3i30000000000000000000000000000000
χ618-808-80222-40-2-2-20400−2i32i3−2i32i3−2i32i30-40000002i3−2i30042i3−2i32i3−2i30000000000000000000000000000000
χ628-808-80222-40-2-2-204002i3−2i32i3−2i32i3−2i30-4000000−2i32i3004−2i32i3−2i32i30000000000000000000000000000000
χ638-808-80-4-4-420444-6-2000000006200000000-66-200000000000000000000000000000000000
χ648-80-4402−1−3i3−1+3i3-40-21+3i31−3i30400−2i32i33+i3−3−i3−3+i33−i3020000002i3−2i300-23−i3−3+i3−3−i33+i30000000000000000000000000000000
χ658-80-4402−1−3i3−1+3i3-40-21+3i31−3i304002i3−2i3−3−i33+i33−i3−3+i302000000−2i32i300-2−3+i33−i33+i3−3−i30000000000000000000000000000000
χ668-80-4402−1+3i3−1−3i3-40-21−3i31+3i30400−2i32i3−3+i33−i33+i3−3−i3020000002i3−2i300-2−3−i33+i33−i3−3+i30000000000000000000000000000000
χ678-80-4402−1+3i3−1−3i3-40-21−3i31+3i304002i3−2i33−i3−3+i3−3−i33+i302000000−2i32i300-23+i3−3−i3−3+i33−i30000000000000000000000000000000
χ688-80-4408-4-480-8440-8000000000-40000000000400000000000000000000000000000000000
χ698-80-440-422204-2-26-200−4i34i32i3−2i32i3−2i3-6-1000000−2i32i3-331i3−i3i3−i30000000000000000000000000000000
χ708-80-440-422204-2-26-2004i3−4i3−2i32i3−2i32i3-6-10000002i3−2i3-331−i3i3−i3i30000000000000000000000000000000
χ718-80-440-422204-2-2-6-200006-6-666-1000000003-31-333-30000000000000000000000000000000
χ728-80-440-422204-2-2-6-20000-666-66-1000000003-313-3-330000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.