Finite Group Databasebeta

← Group #11751734

Character table — Group #11751734

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112224444455668888101010121212122020202020202030306060112224444455668888101010121212122020202020202030306060
order1234651012202044881530606021212404040406882424242488882264610101220204488303060602121240404040688242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-111-1-111111111111111111111111111-1-1-1-1-1-111-1-1
χ3111111111111-1-11111111-1-1-1-11111111-1-1-1-1111111111111-1-11111111-1-1-1-11111111-1-1-1-1
χ4111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111
χ51111111111-1-1111111-1-1-11111-1i−iii−i−i-1-1i−i1111111111-1-1111111-1-1-11111-1i−iii−i−i-1-1i−i
χ61111111111-1-1111111-1-1-11111-1−ii−i−iii-1-1−ii1111111111-1-1111111-1-1-11111-1−ii−i−iii-1-1−ii
χ71111111111-1-1-1-11111-1-1-1-1-1-1-1-1i−iii−i−i11−ii1111111111-1-1-1-11111-1-1-1-1-1-1-1-1i−iii−i−i11−ii
χ81111111111-1-1-1-11111-1-1-1-1-1-1-1-1−ii−i−iii11i−i1111111111-1-1-1-11111-1-1-1-1-1-1-1-1−ii−i−iii11i−i
χ9222-2222-2-2-2220022-2-2-2220000-20000000000222-2222-2-2-2220022-2-2-2220000-20000000000
χ10222-2222-2-2-2-2-20022-2-22-2-2000020000000000222-2222-2-2-2-2-20022-2-22-2-2000020000000000
χ1122-12-122-1222200-1-1-1-12-1-10000-122-1-1-1-1000022-12-122-1222200-1-1-1-12-1-10000-122-1-1-1-10000
χ1222-12-122-1222200-1-1-1-12-1-10000-1-2-21111000022-12-122-1222200-1-1-1-12-1-10000-1-2-211110000
χ1322-12-122-122-2-200-1-1-1-1-211000012i−2i−i−iii000022-12-122-122-2-200-1-1-1-1-211000012i−2i−i−iii0000
χ1422-12-122-122-2-200-1-1-1-1-21100001−2i2iii−i−i000022-12-122-122-2-200-1-1-1-1-21100001−2i2iii−i−i0000
χ1522-1-2-1221-2-22200-1-111-2-1-10000100−i3i3−i3i3000022-1-2-1221-2-22200-1-111-2-1-10000100−i3i3−i3i30000
χ1622-1-2-1221-2-22200-1-111-2-1-10000100i3−i3i3−i3000022-1-2-1221-2-22200-1-111-2-1-10000100i3−i3i3−i30000
χ1722-1-2-1221-2-2-2-200-1-1112110000-1003−3−33000022-1-2-1221-2-2-2-200-1-1112110000-1003−3−330000
χ1822-1-2-1221-2-2-2-200-1-1112110000-100−333−3000022-1-2-1221-2-2-2-200-1-1112110000-100−333−30000
χ192-220-22-20002i−2i2−22-20002i−2i22−2−20000000−i2i2002-220-22-20002i−2i2−22-20002i−2i22−2−20000000−i2i200
χ202-220-22-20002i−2i−222-20002i−2i−2−2220000000i2−i2002-220-22-20002i−2i−222-20002i−2i−2−2220000000i2−i200
χ212-220-22-2000−2i2i2−22-2000−2i2i22−2−20000000i2−i2002-220-22-2000−2i2i2−22-2000−2i2i22−2−20000000i2−i200
χ222-220-22-2000−2i2i−222-2000−2i2i−2−2220000000−i2i2002-220-22-2000−2i2i−222-2000−2i2i−2−2220000000−i2i200
χ2344444-1-14-1-10044-1-1-1-1000-1-1-1-10000000000044444-1-14-1-10044-1-1-1-1000-1-1-1-100000000000
χ2444444-1-14-1-100-4-4-1-1-1-100011110000000000044444-1-14-1-100-4-4-1-1-1-1000111100000000000
χ25444-44-1-1-4110000-1-111000−i5i5−i5i500000000000444-44-1-1-4110000-1-111000−i5i5−i5i500000000000
χ26444-44-1-1-4110000-1-111000i5−i5i5−i500000000000444-44-1-1-4110000-1-111000i5−i5i5−i500000000000
χ274-440-4-110−i5i50022−22-11−i5i5000−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119000000000004-440-4-110−i5i50022−22-11−i5i5000−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ11900000000000
χ284-440-4-110−i5i500−2222-11−i5i5000ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119000000000004-440-4-110−i5i500−2222-11−i5i5000ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ11900000000000
χ294-440-4-110i5−i50022−22-11i5−i5000ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109000000000004-440-4-110i5−i50022−22-11i5−i5000ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ10900000000000
χ304-440-4-110i5−i500−2222-11i5−i5000−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109000000000004-440-4-110i5−i500−2222-11i5−i5000−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ10900000000000
χ314-4-2024-40004i−4i00-22000−2i2i0000000000000004-4-2024-40004i−4i00-22000−2i2i000000000000000
χ324-4-2024-4000−4i4i00-220002i−2i0000000000000004-4-2024-4000−4i4i00-220002i−2i000000000000000
χ3388-48-4-2-2-4-2-20000111100000000000000000088-48-4-2-2-4-2-200001111000000000000000000
χ3488-4-8-4-2-2422000011-1-100000000000000000088-4-8-4-2-2422000011-1-1000000000000000000
χ358-8-404-220−2i52i500001-1i5−i50000000000000000008-8-404-220−2i52i500001-1i5−i5000000000000000000
χ368-8-404-2202i5−2i500001-1−i5i50000000000000000008-8-404-2202i5−2i500001-1−i5i5000000000000000000
χ37111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3811111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ39111111111111-1-11111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111
χ40111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-111111111-1-1
χ411111111111-1-1111111-1-1-11111-1i−iii−i−i-1-1i−i-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-11−ii−i−iii11−ii
χ421111111111-1-1111111-1-1-11111-1−ii−i−iii-1-1−ii-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-11i−iii−i−i11i−i
χ431111111111-1-1-1-11111-1-1-1-1-1-1-1-1i−iii−i−i11−ii-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111−ii−i−iii-1-1i−i
χ441111111111-1-1-1-11111-1-1-1-1-1-1-1-1−ii−i−iii11i−i-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111i−iii−i−i-1-1−ii
χ45222-2222-2-2-2220022-2-2-2220000-20000000000-2-2-22-2-2-2222-2-200-2-2222-2-2000020000000000
χ46222-2222-2-2-2-2-20022-2-22-2-2000020000000000-2-2-22-2-2-22222200-2-222-2220000-20000000000
χ4722-12-122-1222200-1-1-1-12-1-10000-122-1-1-1-10000-2-21-21-2-21-2-2-2-2001111-21100001-2-211110000
χ4822-12-122-1222200-1-1-1-12-1-10000-1-2-211110000-2-21-21-2-21-2-2-2-2001111-2110000122-1-1-1-10000
χ4922-12-122-122-2-200-1-1-1-1-211000012i−2i−i−iii0000-2-21-21-2-21-2-2220011112-1-10000-1−2i2iii−i−i0000
χ5022-12-122-122-2-200-1-1-1-1-21100001−2i2iii−i−i0000-2-21-21-2-21-2-2220011112-1-10000-12i−2i−i−iii0000
χ5122-1-2-1221-2-22200-1-111-2-1-10000100−i3i3−i3i30000-2-2121-2-2-122-2-20011-1-12110000-100i3−i3i3−i30000
χ5222-1-2-1221-2-22200-1-111-2-1-10000100i3−i3i3−i30000-2-2121-2-2-122-2-20011-1-12110000-100−i3i3−i3i30000
χ5322-1-2-1221-2-2-2-200-1-1112110000-1003−3−330000-2-2121-2-2-122220011-1-1-2-1-10000100−333−30000
χ5422-1-2-1221-2-2-2-200-1-1112110000-100−333−30000-2-2121-2-2-122220011-1-1-2-1-100001003−3−330000
χ552-220-22-20002i−2i2−22-20002i−2i22−2−20000000−i2i200-22-202-22000−2i2i−22-22000−2i2i−2−2220000000i2−i200
χ562-220-22-20002i−2i−222-20002i−2i−2−2220000000i2−i200-22-202-22000−2i2i2−2-22000−2i2i22−2−20000000−i2i200
χ572-220-22-2000−2i2i2−22-2000−2i2i22−2−20000000i2−i200-22-202-220002i−2i−22-220002i−2i−2−2220000000−i2i200
χ582-220-22-2000−2i2i−222-2000−2i2i−2−2220000000−i2i200-22-202-220002i−2i2−2-220002i−2i22−2−20000000i2−i200
χ5944444-1-14-1-10044-1-1-1-1000-1-1-1-100000000000-4-4-4-4-411-41100-4-41111000111100000000000
χ6044444-1-14-1-100-4-4-1-1-1-1000111100000000000-4-4-4-4-411-41100441111000-1-1-1-100000000000
χ61444-44-1-1-4110000-1-111000−i5i5−i5i500000000000-4-4-44-4114-1-1000011-1-1000i5−i5i5−i500000000000
χ62444-44-1-1-4110000-1-111000i5−i5i5−i500000000000-4-4-44-4114-1-1000011-1-1000−i5i5−i5i500000000000
χ634-440-4-110−i5i50022−22-11−i5i5000−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ11900000000000-44-4041-10i5−i500−22221-1i5−i5000ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ11900000000000
χ644-440-4-110−i5i500−2222-11−i5i5000ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ11900000000000-44-4041-10i5−i50022−221-1i5−i5000−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ11900000000000
χ654-440-4-110i5−i50022−22-11i5−i5000ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ10900000000000-44-4041-10−i5i500−22221-1−i5i5000−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ10900000000000
χ664-440-4-110i5−i500−2222-11i5−i5000−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ10900000000000-44-4041-10−i5i50022−221-1−i5i5000ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ10900000000000
χ674-4-2024-40004i−4i00-22000−2i2i000000000000000-4420-2-44000−4i4i002-20002i−2i000000000000000
χ684-4-2024-4000−4i4i00-220002i−2i000000000000000-4420-2-440004i−4i002-2000−2i2i000000000000000
χ6988-48-4-2-2-4-2-200001111000000000000000000-8-84-84224220000-1-1-1-1000000000000000000
χ7088-4-8-4-2-2422000011-1-1000000000000000000-8-848422-4-2-20000-1-111000000000000000000
χ718-8-404-220−2i52i500001-1i5−i5000000000000000000-8840-42-202i5−2i50000-11−i5i5000000000000000000
χ728-8-404-2202i5−2i500001-1−i5i5000000000000000000-8840-42-20−2i52i50000-11i5−i5000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.