Finite Group Databasebeta

← Group #11920359

Character table — Group #11920359

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size112223344444466688888888121212121212161616161616161616242432323232323236363636727272727272
order12346222481224244666999121818182481224243636367272727272726121818183636362444224488
χ1111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111-1-11-1-11111111-11111-1-11-1-1111-1-1-1-1-1-11-1111-1-1-111111-11-1-1-1
χ411111111-1-11-1-11111111-11111-1-11-1-1111-1-1-1-1-1-11-1111-1-1-1-1-1-1-1-11-1111
χ51111111-11-11-1-1111-11111111-11-11-1-1111-1-1-1-1-1-1-11-1-1-11111111-11-11-1-1
χ61111111-11-11-1-1111-11111111-11-11-1-1111-1-1-1-1-1-1-11-1-1-1111-1-1-1-11-11-111
χ71111111-1-11111111-1111-1111-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ81111111-1-11111111-1111-1111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ922222222222222222-1-1-12-1-1-1222222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-10000000000
χ1022222222-2-22-2-22222-1-1-1-2-1-1-12-2-22-2-2-1-1-11111112-2-1-1-11110000000000
χ112222222-22-22-2-2222-2-1-1-12-1-1-1-22-22-2-2-1-1-1111111-22111-1-1-10000000000
χ122222222-2-22222222-2-1-1-1-2-1-1-1-2-22222-1-1-1-1-1-1-1-1-1-2-21111110000000000
χ13222-2222000-200-22202220222000-200-2-2-2000000000000002-2-22000000
χ14222-2222000-200-22202220222000-200-2-2-200000000000000-222-2000000
χ1522-12-122222-1-1-12-1-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68222-1-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ680000000000
χ1622-12-122222-1-1-12-1-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68222-1-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ680000000000
χ1722-12-122222-1-1-12-1-1-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52222-1-1-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52-1-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ520000000000
χ1822-12-1222-2-2-1112-1-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ681ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ682-2-2-111ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68-11ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ680000000000
χ1922-12-1222-2-2-1112-1-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ681ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ682-2-2-111ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68-11ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ680000000000
χ2022-12-1222-2-2-1112-1-1-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ521−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ522-2-2-111−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52-11−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ520000000000
χ2122-12-122-22-2-1112-1-11ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-22-2-111ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ681-1−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ680000000000
χ2222-12-122-22-2-1112-1-11ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68-22-2-111ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ681-1−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ680000000000
χ2322-12-122-22-2-1112-1-11−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52-22-2-111−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ521-1ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ520000000000
χ2422-12-122-2-22-1-1-12-1-11ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ681ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-2-22-1-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ6811−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ680000000000
χ2522-12-122-2-22-1-1-12-1-11ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ681ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68-2-22-1-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ6811−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ680000000000
χ2622-12-122-2-22-1-1-12-1-11−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ521−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52-2-22-1-1-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ5211ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ520000000000
χ2733333-1-1333333-1-1-130003000-1-1-1-1-1-1000000000-1-100000011-1-111-1-11-1
χ2833333-1-1333333-1-1-130003000-1-1-1-1-1-1000000000-1-1000000-1-111-1-111-11
χ2933333-1-13-3-33-3-3-1-1-13000-3000-111-111000000000-1100000011-1-11-1-11-11
χ3033333-1-13-3-33-3-3-1-1-13000-3000-111-111000000000-11000000-1-111-111-11-1
χ3133333-1-1-33-33-3-3-1-1-1-300030001-11-1110000000001-100000011-1-1-111-1-11
χ3233333-1-1-33-33-3-3-1-1-1-300030001-11-1110000000001-1000000-1-1111-1-111-1
χ3333333-1-1-3-33333-1-1-1-3000-300011-1-1-1-10000000001100000011-1-1-1-1111-1
χ3433333-1-1-3-33333-1-1-1-3000-300011-1-1-1-100000000011000000-1-11111-1-1-11
χ35444-4444000-400-4440-2-2-20-2-2-2000-400222000000000000000000000000
χ3644-2-4-244000200-4-2-202ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52−2ζ4−2ζ6802ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52−2ζ4−2ζ68000200−2ζ44+2ζ52−2ζ68−2ζ4+2ζ44−2ζ522ζ4+2ζ68000000000000000000000000
χ3744-2-4-244000200-4-2-202ζ4−2ζ44+2ζ52−2ζ4−2ζ682ζ44−2ζ52+2ζ6802ζ4−2ζ44+2ζ52−2ζ4−2ζ682ζ44−2ζ52+2ζ68000200−2ζ4+2ζ44−2ζ522ζ4+2ζ68−2ζ44+2ζ52−2ζ68000000000000000000000000
χ3844-2-4-244000200-4-2-20−2ζ4−2ζ682ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ520−2ζ4−2ζ682ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ520002002ζ4+2ζ68−2ζ44+2ζ52−2ζ68−2ζ4+2ζ44−2ζ52000000000000000000000000
χ394-440-4-4400000004-404440-4-4-4000000000000000000000000000000000
χ404-440-4-4400000004-40-2-2-202220000000006−66−66−6000000000000000000
χ414-440-4-4400000004-40-2-2-20222000000000−66−66−66000000000000000000
χ424-4-202-4400006−60-2202ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52−2ζ4−2ζ680−2ζ44+2ζ52−2ζ68−2ζ4+2ζ44−2ζ522ζ4+2ζ6800006−6000ζ5+ζ7+ζ23+ζ53+ζ61+ζ71−ζ5−ζ7−ζ23−ζ53−ζ61−ζ71−ζ7−ζ13−ζ31−ζ53−ζ61−ζ71ζ7+ζ13+ζ31+ζ53+ζ61+ζ71−ζ5+ζ13−ζ23+ζ31ζ5−ζ13+ζ23−ζ31000000000000000000
χ434-4-202-4400006−60-2202ζ4−2ζ44+2ζ52−2ζ4−2ζ682ζ44−2ζ52+2ζ680−2ζ4+2ζ44−2ζ522ζ4+2ζ68−2ζ44+2ζ52−2ζ6800006−6000−ζ7−ζ13−ζ31−ζ53−ζ61−ζ71ζ7+ζ13+ζ31+ζ53+ζ61+ζ71−ζ5+ζ13−ζ23+ζ31ζ5−ζ13+ζ23−ζ31ζ5+ζ7+ζ23+ζ53+ζ61+ζ71−ζ5−ζ7−ζ23−ζ53−ζ61−ζ71000000000000000000
χ444-4-202-4400006−60-220−2ζ4−2ζ682ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ5202ζ4+2ζ68−2ζ44+2ζ52−2ζ68−2ζ4+2ζ44−2ζ5200006−6000−ζ5+ζ13−ζ23+ζ31ζ5−ζ13+ζ23−ζ31ζ5+ζ7+ζ23+ζ53+ζ61+ζ71−ζ5−ζ7−ζ23−ζ53−ζ61−ζ71−ζ7−ζ13−ζ31−ζ53−ζ61−ζ71ζ7+ζ13+ζ31+ζ53+ζ61+ζ71000000000000000000
χ454-4-202-440000−660-2202ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52−2ζ4−2ζ680−2ζ44+2ζ52−2ζ68−2ζ4+2ζ44−2ζ522ζ4+2ζ680000−66000−ζ5−ζ7−ζ23−ζ53−ζ61−ζ71ζ5+ζ7+ζ23+ζ53+ζ61+ζ71ζ7+ζ13+ζ31+ζ53+ζ61+ζ71−ζ7−ζ13−ζ31−ζ53−ζ61−ζ71ζ5−ζ13+ζ23−ζ31−ζ5+ζ13−ζ23+ζ31000000000000000000
χ464-4-202-440000−660-2202ζ4−2ζ44+2ζ52−2ζ4−2ζ682ζ44−2ζ52+2ζ680−2ζ4+2ζ44−2ζ522ζ4+2ζ68−2ζ44+2ζ52−2ζ680000−66000ζ7+ζ13+ζ31+ζ53+ζ61+ζ71−ζ7−ζ13−ζ31−ζ53−ζ61−ζ71ζ5−ζ13+ζ23−ζ31−ζ5+ζ13−ζ23+ζ31−ζ5−ζ7−ζ23−ζ53−ζ61−ζ71ζ5+ζ7+ζ23+ζ53+ζ61+ζ71000000000000000000
χ474-4-202-440000−660-220−2ζ4−2ζ682ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ5202ζ4+2ζ68−2ζ44+2ζ52−2ζ68−2ζ4+2ζ44−2ζ520000−66000ζ5−ζ13+ζ23−ζ31−ζ5+ζ13−ζ23+ζ31−ζ5−ζ7−ζ23−ζ53−ζ61−ζ71ζ5+ζ7+ζ23+ζ53+ζ61+ζ71ζ7+ζ13+ζ31+ζ53+ζ61+ζ71−ζ7−ζ13−ζ31−ζ53−ζ61−ζ71000000000000000000
χ48666-66-2-2000-6002-2-200000000000200000000000000000002-22-2000000
χ49666-66-2-2000-6002-2-20000000000020000000000000000000-22-22000000
χ5066-36-3-2-2666-3-3-3-211-3000-3000-2-2-2111000000000110000000000000000
χ5166-36-3-2-26-6-6-333-211-30003000-2221-1-10000000001-10000000000000000
χ5266-36-3-2-2-66-6-333-2113000-30002-221-1-1000000000-110000000000000000
χ5366-36-3-2-2-6-66-3-3-3-2113000300022-2111000000000-1-10000000000000000
χ541212-6-12-6-4-400060042200000000000-200000000000000000000000000000
χ5512-12120-124-40000000-4400000000000000000000000000000000000000000
χ5612-12-6064-4000036−3602-2000000000000−66000000000000000000000000000
χ5712-12-6064-40000−363602-20000000000006−6000000000000000000000000000

Here ζ is a primitive root of unity of order 72 (ζ72 = 1).