Finite Group Databasebeta

← Group #13088439

Character table — Group #13088439

Order 1440.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size112222444455668888101010101010121216161820202020202020202020242424242424303030303030454545456060606060607290
order1233663561044241515303088121212126121530212122424242424242424102030306060248888888861224242424104
χ1111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111-1-111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ31111111111111-111111111111-111-111111111111-111-1-1-1111-1-1-1-1-1-1-1111-1-1-1-1
χ41111111111111-11111-1-111111-111-111-1-1-1-1-1-1-1-11-111-1-1-11-1-1111111-11-1-111-1-1
χ5111111111111-111111111111-1111-11111111111-11-1-1111-1-1-111-1-1-1-11-1-1-111-1-1
χ6111111111111-111111-1-11111-1111-111-1-1-1-1-1-1-1-1-11-1-1111-111-1-111111-111-1-1-1-1
χ7111111111111-1-11111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ8111111111111-1-11111-1-11111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ91111111111-1-1111111i−i-1-1-1-111111-1-1ii−i−iii−i−i111111-1-1i−ii−iii−i−i-1-1i−ii−i1-1
χ101111111111-1-1111111−ii-1-1-1-111111-1-1−i−iii−i−iii111111-1-1−ii−ii−i−iii-1-1−ii−ii1-1
χ111111111111-1-11-11111i−i-1-1-1-11-111-1-1-1ii−i−iii−i−i1-111-1-11-1i−i−ii−i−iii1-1i−i−ii-11
χ121111111111-1-11-11111−ii-1-1-1-11-111-1-1-1−i−iii−i−iii1-111-1-11-1−iii−iii−i−i1-1−iii−i-11
χ131111111111-1-1-111111i−i-1-1-1-1-1111-1-1-1ii−i−iii−i−i-11-1-111-11−iii−i−i−iii-11−iii−i-11
χ141111111111-1-1-111111−ii-1-1-1-1-1111-1-1-1−i−iii−i−iii-11-1-111-11i−i−iiii−i−i-11i−i−ii-11
χ151111111111-1-1-1-11111i−i-1-1-1-1-1-1111-1-1ii−i−iii−i−i-1-1-1-1-1-111−ii−iiii−i−i11−ii−ii1-1
χ161111111111-1-1-1-11111−ii-1-1-1-1-1-1111-1-1−i−iii−i−iii-1-1-1-1-1-111i−ii−i−i−iii11i−ii−i1-1
χ17222-1-12-12-122202-122-122-1-1220-1-1-10-1-12-12-1-1-1-1-10200-1-12000220000-1000-1-100
χ18222-1-12-12-122202-122-1-2-2-1-1220-1-1-10-1-1-21-2111110200-1-12000-2-20000-10001100
χ19222-1-12-12-12220-2-122-122-1-12201-1-10-1-12-12-1-1-1-1-10-20011-2000-2-2000010001100
χ20222-1-12-12-12220-2-122-1-2-2-1-12201-1-10-1-1-21-2111110-20011-20002200001000-1-100
χ21222-1-12-12-12-2-202-122-12i−2i11-2-20-1-1-10112i−i−2ii−i−iii0200-1-1-20002i−2i00001000−ii00
χ22222-1-12-12-12-2-202-122-1−2i2i11-2-20-1-1-1011−2ii2i−iii−i−i0200-1-1-2000−2i2i00001000i−i00
χ23222-1-12-12-12-2-20-2-122-12i−2i11-2-201-1-10112i−i−2ii−i−iii0-200112000−2i2i0000-1000i−i00
χ24222-1-12-12-12-2-20-2-122-1−2i2i11-2-201-1-1011−2ii2i−iii−i−i0-2001120002i−2i0000-1000−ii00
χ2522-122-1-12-1222202-1-122222-1-1-10-1-10-1-1-12-12-1-1-1-120-1-10002220000000-1-1-10000
χ2622-122-1-12-1222202-1-12-2-222-1-1-10-1-10-1-11-21-2111120-1-10002-2-20000000-1110000
χ2722-122-1-12-1222-202-1-122222-1-110-1-10-1-1-12-12-1-1-1-1-2011000-2-2-200000001110000
χ2822-122-1-12-1222-202-1-12-2-222-1-110-1-10-1-11-21-21111-2011000-22200000001-1-10000
χ2922-122-1-12-12-2-2202-1-122i−2i-2-211-10-1-1011−i2ii−2i−i−iii20-1-1000-22i−2i00000001−ii0000
χ3022-122-1-12-12-2-2202-1-12−2i2i-2-211-10-1-1011i−2i−i2iii−i−i20-1-1000-2−2i2i00000001i−i0000
χ3122-122-1-12-12-2-2-202-1-122i−2i-2-21110-1-1011−i2ii−2i−i−iii-20110002−2i2i0000000-1i−i0000
χ3222-122-1-12-12-2-2-202-1-12−2i2i-2-21110-1-1011i−2i−i2iii−i−i-201100022i−2i0000000-1−ii0000
χ332-222-2-222-2-22i−2i0022-2-2002i−2i2i−2i002-202i−2i000000000000000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ10900000000
χ342-222-2-222-2-22i−2i0022-2-2002i−2i2i−2i002-202i−2i00000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900000000
χ352-222-2-222-2-2−2i2i0022-2-200−2i2i−2i2i002-20−2i2i00000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900000000
χ362-222-2-222-2-2−2i2i0022-2-200−2i2i−2i2i002-20−2i2i000000000000000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ11900000000
χ374444444-14-10044-1-1-1-100000044-1-140000000000-1-1-1-1-1-10000000000000000-10
χ384444444-14-1004-4-1-1-1-10000004-4-1-1-40000000000-11-1-111000000000000000010
χ394444444-14-100-44-1-1-1-1000000-44-1-1-400000000001-111-1-1000000000000000010
χ404444444-14-100-4-4-1-1-1-1000000-4-4-1-1400000000001111110000000000000000-10
χ4144-2-2-2-214144400-2-2-2-244-2-2-2-20011011-2-2-2-21111000000000000000000000000
χ4244-2-2-2-214144400-2-2-2-2-4-4-2-2-2-200110112222-1-1-1-1000000000000000000000000
χ4344-2-2-2-21414-4-400-2-2-2-24i−4i222200110-1-1−2i−2i2i2iii−i−i000000000000000000000000
χ4444-2-2-2-21414-4-400-2-2-2-2−4i4i222200110-1-12i2i−2i−2i−i−iii000000000000000000000000
χ454-44-22-4-242-44i−4i00-24-4200−2i2i4i−4i00-220−2i2i00000000000000000000000000000000
χ464-44-22-4-242-4−4i4i00-24-42002i−2i−4i4i00-2202i−2i00000000000000000000000000000000
χ474-4-24-42-242-44i−4i004-22-4004i−4i−2i2i00-220−2i2i00000000000000000000000000000000
χ484-4-24-42-242-4−4i4i004-22-400−4i4i2i−2i00-2202i−2i00000000000000000000000000000000
χ494-4-2-22214-1-44i−4i00-2-22200−2i2i−2i2i001-10i−i00003ζ7+3ζ23+3ζ31+3ζ47+3ζ71+3ζ79+3ζ103+3ζ119−3ζ7−3ζ23−3ζ31−3ζ47−3ζ71−3ζ79−3ζ103−3ζ119−3ζ13−3ζ29−3ζ37−3ζ53−3ζ61−3ζ77−3ζ101−3ζ1093ζ13+3ζ29+3ζ37+3ζ53+3ζ61+3ζ77+3ζ101+3ζ109000000000000000000000000
χ504-4-2-22214-1-44i−4i00-2-22200−2i2i−2i2i001-10i−i0000−3ζ7−3ζ23−3ζ31−3ζ47−3ζ71−3ζ79−3ζ103−3ζ1193ζ7+3ζ23+3ζ31+3ζ47+3ζ71+3ζ79+3ζ103+3ζ1193ζ13+3ζ29+3ζ37+3ζ53+3ζ61+3ζ77+3ζ101+3ζ109−3ζ13−3ζ29−3ζ37−3ζ53−3ζ61−3ζ77−3ζ101−3ζ109000000000000000000000000
χ514-4-2-22214-1-4−4i4i00-2-222002i−2i2i−2i001-10−ii0000−3ζ13−3ζ29−3ζ37−3ζ53−3ζ61−3ζ77−3ζ101−3ζ1093ζ13+3ζ29+3ζ37+3ζ53+3ζ61+3ζ77+3ζ101+3ζ1093ζ7+3ζ23+3ζ31+3ζ47+3ζ71+3ζ79+3ζ103+3ζ119−3ζ7−3ζ23−3ζ31−3ζ47−3ζ71−3ζ79−3ζ103−3ζ119000000000000000000000000
χ524-4-2-22214-1-4−4i4i00-2-222002i−2i2i−2i001-10−ii00003ζ13+3ζ29+3ζ37+3ζ53+3ζ61+3ζ77+3ζ101+3ζ109−3ζ13−3ζ29−3ζ37−3ζ53−3ζ61−3ζ77−3ζ101−3ζ109−3ζ7−3ζ23−3ζ31−3ζ47−3ζ71−3ζ79−3ζ103−3ζ1193ζ7+3ζ23+3ζ31+3ζ47+3ζ71+3ζ79+3ζ103+3ζ119000000000000000000000000
χ53888-4-48-4-2-4-200081-2-210000000-411000000000000-20011000000000000000000
χ54888-4-48-4-2-4-2000-81-2-210000000411000000000000200-1-1000000000000000000
χ5588-488-4-4-2-4-20080-211-2000000-401100000000000-201100000000000000000000
χ5688-488-4-4-2-4-200-80-211-200000040110000000000020-1-100000000000000000000
χ578-888-8-88-2-820000-2-22200000000-2200000000000000000000000000000000000
χ588-88-44-8-4-24200001-22-1000000001-1000000000000000−1515000000000000000000
χ598-88-44-8-4-24200001-22-1000000001-100000000000000015−15000000000000000000
χ608-8-48-84-4-2420000-21-12000000001-10000000000000−i15i1500000000000000000000
χ618-8-48-84-4-2420000-21-12000000001-10000000000000i15−i1500000000000000000000
χ621616-8-8-8-84-44-40000222200000000-1-100000000000000000000000000000000000
χ6316-16-8-8884-4-44000022-2-200000000-1100000000000000000000000000000000000

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