Finite Group Databasebeta

← Group #11751810

Character table — Group #11751810

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222244444455558888888888101010101010121220202020202020202020202020202424242430303030303030306060
order122234466651010101212444415202030303060606060441212121244888812122424242424242424202020208888888824
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111-1-1-1-11111111111-1-1-1-1-1-111ii−i−i-1-1iiii−i−i−i−i1111iiii−i−i−i−i-1-1
χ61111111111111111-1-1-1-11111111111-1-1-1-1-1-111−i−iii-1-1−i−i−i−iiiii1111−i−i−i−iiiii-1-1
χ71111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i-1-1-1-1−i−i−i−iiiii11
χ81111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii-1-1-1-1iiii−i−i−i−i11
χ911111-1-11111111-1-111111-1-1111-1-1-1-1-1-111111-11-11-1-1-111-1-111-1-1-1-11111-1-111-1-1-11
χ1011111-1-11111111-1-111111-1-1111-1-1-1-1-1-111111-1-11-11-1-1-1-111-1-111-1-111-1-111-1-111-11
χ1111111-1-11111111-1-111111-1-1111-1-1-1-1-1-11111-111-11-1-1-111-1-111-1-111-1-1-1-111-1-1111-1
χ1211111-1-11111111-1-111111-1-1111-1-1-1-1-1-11111-11-11-11-1-1-1-111-1-11111-1-111-1-111-1-11-1
χ1311111-1-11111111-1-1-1-1-1-11-1-1111-1-1-1-111-1-1-1-11-1i−i−ii11ii−i−i−i−iii-1-111ii−i−i−i−iii1-1
χ1411111-1-11111111-1-1-1-1-1-11-1-1111-1-1-1-111-1-1-1-11-1−iii−i11−i−iiiii−i−i-1-111−i−iiiii−i−i1-1
χ1511111-1-11111111-1-1-1-1-1-11-1-1111-1-1-1-111-1-1-1-1-11i−i−ii11ii−i−i−i−iii11-1-1−i−iiiii−i−i-11
χ1611111-1-11111111-1-1-1-1-1-11-1-1111-1-1-1-111-1-1-1-1-11−iii−i11−i−iiiii−i−i11-1-1ii−i−i−i−iii-11
χ172222-122-1-1-12222-1-12222-122-1-1-1-1-1-1-122-1-1-1-1002222-1-1-1-1-1-1-1-1-1-100000000000000
χ182222-122-1-1-12222-1-12222-122-1-1-1-1-1-1-122-1-1-1-100-2-2-2-2-1-11111111100000000000000
χ192222-122-1-1-12222-1-1-2-2-2-2-122-1-1-1-1-1-1-1-2-21111002i2i−2i−2i11−i−i−i−iiiii00000000000000
χ202222-122-1-1-12222-1-1-2-2-2-2-122-1-1-1-1-1-1-1-2-2111100−2i−2i2i2i11iiii−i−i−i−i00000000000000
χ212222-1-2-2-1-1-12222112222-1-2-2-1-1-11111-2-2-1-1-1-1002-22-211-1-111-1-11100000000000000
χ222222-1-2-2-1-1-12222112222-1-2-2-1-1-11111-2-2-1-1-1-100-22-221111-1-111-1-100000000000000
χ232222-1-2-2-1-1-1222211-2-2-2-2-1-2-2-1-1-11111221111002i−2i−2i2i-1-1−i−iiiii−i−i00000000000000
χ242222-1-2-2-1-1-1222211-2-2-2-2-1-2-2-1-1-1111122111100−2i2i2i−2i-1-1ii−i−i−i−iii00000000000000
χ2522-2-22002-2-22-2-22002i2i−2i−2i200-2-220000002i2i−2i−2i0000000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900
χ2622-2-22002-2-22-2-22002i2i−2i−2i200-2-220000002i2i−2i−2i00000000000000000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ11900
χ2722-2-22002-2-22-2-2200−2i−2i2i2i200-2-22000000−2i−2i2i2i00000000000000000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ10900
χ2822-2-22002-2-22-2-2200−2i−2i2i2i200-2-22000000−2i−2i2i2i0000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900
χ292-22-222i−2i-22-22-22-22i−2i2-22-222i−2i2-2-22i2i−2i−2i2i−2i2-22-20000002i−2i0000000000000000000000
χ302-22-222i−2i-22-22-22-22i−2i-22-2222i−2i2-2-22i2i−2i−2i−2i2i-22-22000000−2i2i0000000000000000000000
χ312-22-22−2i2i-22-22-22-2−2i2i2-22-22−2i2i2-2-2−2i−2i2i2i−2i2i2-22-2000000−2i2i0000000000000000000000
χ322-22-22−2i2i-22-22-22-2−2i2i-22-222−2i2i2-2-2−2i−2i2i2i2i−2i-22-220000002i−2i0000000000000000000000
χ332-22-2-12i−2i1-112-22-2−ii2-22-2-12i−2i-111−i−iii2i−2i-11-11000000−ii−i3i33−3−i3i33−300000000000000
χ342-22-2-12i−2i1-112-22-2−ii2-22-2-12i−2i-111−i−iii2i−2i-11-11000000−iii3−i3−33i3−i3−3300000000000000
χ352-22-2-12i−2i1-112-22-2−ii-22-22-12i−2i-111−i−iii−2i2i1-11-1000000i−i3−3i3−i3−33−i3i300000000000000
χ362-22-2-12i−2i1-112-22-2−ii-22-22-12i−2i-111−i−iii−2i2i1-11-1000000i−i−33−i3i33−3i3−i300000000000000
χ372-22-2-1−2i2i1-112-22-2i−i2-22-2-1−2i2i-111ii−i−i−2i2i-11-11000000i−i−i3i3−33−i3i3−3300000000000000
χ382-22-2-1−2i2i1-112-22-2i−i2-22-2-1−2i2i-111ii−i−i−2i2i-11-11000000i−ii3−i33−3i3−i33−300000000000000
χ392-22-2-1−2i2i1-112-22-2i−i-22-22-1−2i2i-111ii−i−i2i−2i1-11-1000000−ii3−3−i3i3−33i3−i300000000000000
χ402-22-2-1−2i2i1-112-22-2i−i-22-22-1−2i2i-111ii−i−i2i−2i1-11-1000000−ii−33i3−i33−3−i3i300000000000000
χ412-2-22200-2-2222-2-2002i−2i−2i2i200-22-20000002i−2i−2i2i00000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1190000
χ422-2-22200-2-2222-2-2002i−2i−2i2i200-22-20000002i−2i−2i2i000000000000000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1190000
χ432-2-22200-2-2222-2-200−2i2i2i−2i200-22-2000000−2i2i2i−2i000000000000000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1090000
χ442-2-22200-2-2222-2-200−2i2i2i−2i200-22-2000000−2i2i2i−2i00000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1090000
χ454444444444-1-1-1-1440000-1-1-1-1-1-1-1-1-1-10000004400000000000000-1-1-1-10000000000
χ464444444444-1-1-1-1440000-1-1-1-1-1-1-1-1-1-1000000-4-40000000000000011110000000000
χ4744444-4-4444-1-1-1-1-4-40000-111-1-1-111110000004-40000000000000011-1-10000000000
χ4844444-4-4444-1-1-1-1-4-40000-111-1-1-11111000000-4400000000000000-1-1110000000000
χ4944-4-4-200-2224-4-44004i4i−4i−4i-20022-2000000−2i−2i2i2i000000000000000000000000000000
χ5044-4-4-200-2224-4-4400−4i−4i4i4i-20022-20000002i2i−2i−2i000000000000000000000000000000
χ514-44-444i−4i-44-4-11-114i−4i0000-1−ii-111−i−iii0000000000000000000000−55−i5i50000000000
χ524-44-444i−4i-44-4-11-114i−4i0000-1−ii-111−i−iii00000000000000000000005−5i5−i50000000000
χ534-44-44−4i4i-44-4-11-11−4i4i0000-1i−i-111ii−i−i0000000000000000000000−55i5−i50000000000
χ544-44-44−4i4i-44-4-11-11−4i4i0000-1i−i-111ii−i−i00000000000000000000005−5−i5i50000000000
χ554-4-44-20022-244-4-4004i−4i−4i4i-2002-22000000−2i2i2i−2i000000000000000000000000000000
χ564-4-44-20022-244-4-400−4i4i4i−4i-2002-220000002i−2i−2i2i000000000000000000000000000000
χ578888-488-4-4-4-2-2-2-2-4-400001-2-21111111000000000000000000000000000000000000
χ588888-4-8-8-4-4-4-2-2-2-2440000122111-1-1-1-1000000000000000000000000000000000000
χ5988-8-88008-8-8-222-2000000-20022-20000000000000000000000000000000000000000
χ6088-8-8-400-444-222-2000000100-1-11−i15i15−i15i15000000000000000000000000000000000000
χ6188-8-8-400-444-222-2000000100-1-11i15−i15i15−i15000000000000000000000000000000000000
χ628-88-8-48i−8i4-44-22-22−4i4i00001−2i2i1-1-1ii−i−i000000000000000000000000000000000000
χ638-88-8-4−8i8i4-44-22-224i−4i000012i−2i1-1-1−i−iii000000000000000000000000000000000000
χ648-8-88800-8-88-2-222000000-2002-220000000000000000000000000000000000000000
χ658-8-88-40044-4-2-222000000100-11-1−151515−15000000000000000000000000000000000000
χ668-8-88-40044-4-2-222000000100-11-115−15−1515000000000000000000000000000000000000

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