Finite Group Databasebeta

← Group #13088670

Character table — Group #13088670

Order 1440.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size112222222224444445588888888888888888101010101010101010101010101818202020202020202020202020202020202020202045454545727290909090
order123333466665101212121244151515152030303030606060606060606028888121212121212121244666624242424242424242424242424242424888820202288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111-1-111111111111111111-1ii−i−i-1-1-1-1-1-1-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i11-1-1i−i
χ611111111111111111-1-111111111111111111-1ii−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii-1-111−ii
χ711111111111111111-1-111111111111111111-1−i−iii-1-1-1-1-1-1-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii11-1-1−ii
χ811111111111111111-1-111111111111111111-1−i−iii-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i-1-111i−i
χ9111111-1111111-1-1-1-1111111-11111-1-1-1-1-1-1-1-1-11-11-1111111111-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-1-1-1
χ10111111-1111111-1-1-1-1111111-11111-1-1-1-1-1-1-1-1-11-11-111111111-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1111
χ11111111-1111111-1-1-1-1111111-11111-1-1-1-1-1-1-1-1-1-11-11111111111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111
χ12111111-1111111-1-1-1-1111111-11111-1-1-1-1-1-1-1-1-1-11-1111111111-11-1-1-1-1-1-1-1-11111-1-1-1-111111111-11-11-1-1
χ13111111-1111111-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-11i−i−ii-1-1-1-1-1-1-1-11-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i1-1-11−ii
χ14111111-1111111-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-11i−i−ii-1-1-1-1-1-1-1-1-111111iiii−i−i−i−i−i−i−i−iiiii−i−iii-111-1i−i
χ15111111-1111111-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-11−iii−i-1-1-1-1-1-1-1-11-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iii1-1-11i−i
χ16111111-1111111-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-11−iii−i-1-1-1-1-1-1-1-1-111111−i−i−i−iiiiiiiii−i−i−i−iii−i−i-111-1−ii
χ17222-1-1-122-1-1-1222-1-1-1222-1-1-122-1-1-122-1-1-1-1-1-12222222-1-1-1-1-1-1002-1-1-12-1-1-12-1-1-12-1-1-12-1-1-10000000000
χ18222-1-1-122-1-1-1222-1-1-1222-1-1-122-1-1-122-1-1-1-1-1-12-2-2-2-222-1-1-1-1-1-1002-1-1-1-2111-2111-2111-21110000000000
χ19222-1-1-122-1-1-1222-1-1-1-2-22-1-1-122-1-1-122-1-1-1-1-1-1-22i2i−2i−2i-2-211111100-21112i−i−i−i2i−i−i−i−2iiii−2iiii0000000000
χ20222-1-1-122-1-1-1222-1-1-1-2-22-1-1-122-1-1-122-1-1-1-1-1-1-2−2i−2i2i2i-2-211111100-2111−2iiii−2iiii2i−i−i−i2i−i−i−i0000000000
χ21222-1-1-1-22-1-1-122-2111222-1-1-1-22-1-1-1-2-2111111-22-22-222-1-1-1-1-1-100-21112-1-1-1-21112-1-1-1-21110000000000
χ22222-1-1-1-22-1-1-122-2111222-1-1-1-22-1-1-1-2-2111111-2-22-2222-1-1-1-1-1-100-2111-21112-1-1-1-21112-1-1-10000000000
χ23222-1-1-1-22-1-1-122-2111-2-22-1-1-1-22-1-1-1-2-211111122i−2i−2i2i-2-2111111002-1-1-12i−i−i−i−2iiii−2iiii2i−i−i−i0000000000
χ24222-1-1-1-22-1-1-122-2111-2-22-1-1-1-22-1-1-1-2-21111112−2i2i2i−2i-2-2111111002-1-1-1−2iiii2i−i−i−i2i−i−i−i−2iiii0000000000
χ2522-12-1-12-12-1-122-12-1-122-12-1-12-12-1-1-1-122-1-1-1-122222-1-122-1-1-1-100-12-1-1-12-1-1-12-1-1-12-1-1-12-1-10000000000
χ2622-12-1-12-12-1-122-12-1-122-12-1-12-12-1-1-1-122-1-1-1-12-2-2-2-2-1-122-1-1-1-100-12-1-11-2111-2111-2111-2110000000000
χ2722-12-1-12-12-1-122-12-1-1-2-2-12-1-12-12-1-1-1-122-1-1-1-1-22i2i−2i−2i11-2-21111001-211−i2i−i−i−i2i−i−ii−2iiii−2iii0000000000
χ2822-12-1-12-12-1-122-12-1-1-2-2-12-1-12-12-1-1-1-122-1-1-1-1-2−2i−2i2i2i11-2-21111001-211i−2iiii−2iii−i2i−i−i−i2i−i−i0000000000
χ2922-12-1-1-2-12-1-1221-21122-12-1-1-2-12-1-111-2-21111-22-22-2-1-122-1-1-1-1001-211-12-1-11-211-12-1-11-2110000000000
χ3022-12-1-1-2-12-1-1221-21122-12-1-1-2-12-1-111-2-21111-2-22-22-1-122-1-1-1-1001-2111-211-12-1-11-211-12-1-10000000000
χ3122-12-1-1-2-12-1-1221-211-2-2-12-1-1-2-12-1-111-2-2111122i−2i−2i2i11-2-2111100-12-1-1−i2i−i−ii−2iiii−2iii−i2i−i−i0000000000
χ3222-12-1-1-2-12-1-1221-211-2-2-12-1-1-2-12-1-111-2-211112−2i2i2i−2i11-2-2111100-12-1-1i−2iii−i2i−i−i−i2i−i−ii−2iii0000000000
χ3322-1-12-12-1-12-122-1-12-122-1-12-12-1-12-1-1-1-1-122-1-122222-1-1-1-122-1-100-1-12-1-1-12-1-1-12-1-1-12-1-1-12-10000000000
χ3422-1-12-12-1-12-122-1-12-122-1-12-12-1-12-1-1-1-1-122-1-12-2-2-2-2-1-1-1-122-1-100-1-12-111-2111-2111-2111-210000000000
χ3522-1-12-12-1-12-122-1-12-1-2-2-1-12-12-1-12-1-1-1-1-122-1-1-22i2i−2i−2i1111-2-2110011-21−i−i2i−i−i−i2i−iii−2iiii−2ii0000000000
χ3622-1-12-12-1-12-122-1-12-1-2-2-1-12-12-1-12-1-1-1-1-122-1-1-2−2i−2i2i2i1111-2-2110011-21ii−2iiii−2ii−i−i2i−i−i−i2i−i0000000000
χ3722-1-12-1-2-1-12-12211-2122-1-12-1-2-1-12-11111-2-211-22-22-2-1-1-1-122-1-10011-21-1-12-111-21-1-12-111-210000000000
χ3822-1-12-1-2-1-12-12211-2122-1-12-1-2-1-12-11111-2-211-2-22-22-1-1-1-122-1-10011-2111-21-1-12-111-21-1-12-10000000000
χ3922-1-12-1-2-1-12-12211-21-2-2-1-12-1-2-1-12-11111-2-21122i−2i−2i2i1111-2-21100-1-12-1−i−i2i−iii−2iiii−2ii−i−i2i−i0000000000
χ4022-1-12-1-2-1-12-12211-21-2-2-1-12-1-2-1-12-11111-2-2112−2i2i2i−2i1111-2-21100-1-12-1ii−2ii−i−i2i−i−i−i2i−iii−2ii0000000000
χ4122-1-1-122-1-1-1222-1-1-1222-1-1-122-1-1-12-1-1-1-1-1-12222222-1-1-1-1-1-12200-1-1-12-1-1-12-1-1-12-1-1-12-1-1-120000000000
χ4222-1-1-122-1-1-1222-1-1-1222-1-1-122-1-1-12-1-1-1-1-1-1222-2-2-2-2-1-1-1-1-1-12200-1-1-12111-2111-2111-2111-20000000000
χ4322-1-1-122-1-1-1222-1-1-12-2-2-1-1-122-1-1-12-1-1-1-1-1-122-22i2i−2i−2i111111-2-200111-2−i−i−i2i−i−i−i2iiii−2iiii−2i0000000000
χ4422-1-1-122-1-1-1222-1-1-12-2-2-1-1-122-1-1-12-1-1-1-1-1-122-2−2i−2i2i2i111111-2-200111-2iii−2iiii−2i−i−i−i2i−i−i−i2i0000000000
χ4522-1-1-12-2-1-1-1222111-222-1-1-12-2-1-1-12111111-2-2-22-22-2-1-1-1-1-1-12200111-2-1-1-12111-2-1-1-12111-20000000000
χ4622-1-1-12-2-1-1-1222111-222-1-1-12-2-1-1-12111111-2-2-2-22-22-1-1-1-1-1-12200111-2111-2-1-1-12111-2-1-1-120000000000
χ4722-1-1-12-2-1-1-1222111-2-2-2-1-1-12-2-1-1-12111111-2-222i−2i−2i2i111111-2-200-1-1-12−i−i−i2iiii−2iiii−2i−i−i−i2i0000000000
χ4822-1-1-12-2-1-1-1222111-2-2-2-1-1-12-2-1-1-12111111-2-22−2i2i2i−2i111111-2-200-1-1-12iii−2i−i−i−i2i−i−i−i2iiii−2i0000000000
χ492-222220-2-2-2-22-200002i−2i22220-2-2-2-200000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119000000
χ502-222220-2-2-2-22-200002i−2i22220-2-2-2-200000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000002ζ13+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+2ζ119000000
χ512-222220-2-2-2-22-20000−2i2i22220-2-2-2-20000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000002ζ7+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+2ζ109000000
χ522-222220-2-2-2-22-20000−2i2i22220-2-2-2-20000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109000000
χ5344444444444-1-1444400-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000044000000000000000000000000-1-10000
χ5444444444444-1-1444400-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000-4-4000000000000000000000000110000
χ55444444-44444-1-1-4-4-4-400-1-1-1-11-1-1-1-11111111100000000000004-4000000000000000000000000-110000
χ56444444-44444-1-1-4-4-4-400-1-1-1-11-1-1-1-1111111110000000000000-440000000000000000000000001-10000
χ574-44-2-2-20-42224-400004i−4i4-2-2-20-422200000000000004i−4i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ584-44-2-2-20-42224-40000−4i4i4-2-2-20-42220000000000000−4i4i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ594-4-24-2-202-4224-400004i−4i-24-2-202-4220000000000000−2i2i4i−4i−2i2i−2i2i00000000000000000000000000000000
χ604-4-24-2-202-4224-40000−4i4i-24-2-202-42200000000000002i−2i−4i4i2i−2i2i−2i00000000000000000000000000000000
χ614-4-2-24-2022-424-400004i−4i-2-24-2022-420000000000000−2i2i−2i2i4i−4i−2i2i00000000000000000000000000000000
χ624-4-2-24-2022-424-40000−4i4i-2-24-2022-4200000000000002i−2i2i−2i−4i4i2i−2i00000000000000000000000000000000
χ634-4-2-2-240222-44-400004i−4i-2-2-240222-40000000000000−2i2i−2i2i−2i2i4i−4i00000000000000000000000000000000
χ644-4-2-2-240222-44-40000−4i4i-2-2-240222-400000000000002i−2i2i−2i2i−2i−4i4i00000000000000000000000000000000
χ65888-4-4-488-4-4-4-2-28-4-4-400-2111-2-2111-2-2111111000000000000000000000000000000000000000000000
χ66888-4-4-4-88-4-4-4-2-2-844400-21112-211122-1-1-1-1-1-1000000000000000000000000000000000000000000000
χ6788-48-4-48-48-4-4-2-2-48-4-4001-211-21-21111-2-21111000000000000000000000000000000000000000000000
χ6888-48-4-4-8-48-4-4-2-24-844001-21121-211-1-122-1-1-1-1000000000000000000000000000000000000000000000
χ6988-4-48-48-4-48-4-2-2-4-48-40011-21-211-211111-2-211000000000000000000000000000000000000000000000
χ7088-4-48-4-8-4-48-4-2-244-840011-21211-21-1-1-1-122-1-1000000000000000000000000000000000000000000000
χ7188-4-4-488-4-4-48-2-2-4-4-4800111-2-2111-2111111-2-2000000000000000000000000000000000000000000000
χ7288-4-4-48-8-4-4-48-2-2444-800111-22111-2-1-1-1-1-1-122000000000000000000000000000000000000000000000
χ738-888880-8-8-8-8-22000000-2-2-2-20222200000000000000000000000000000000000000000000000000000
χ748-88-4-4-40-8444-22000000-211102-1-1-100−1515−1515−1515000000000000000000000000000000000000000000000
χ758-88-4-4-40-8444-22000000-211102-1-1-10015−1515−1515−15000000000000000000000000000000000000000000000
χ768-8-48-4-404-844-220000001-2110-12-1-1−151500−151515−15000000000000000000000000000000000000000000000
χ778-8-48-4-404-844-220000001-2110-12-1-115−150015−15−1515000000000000000000000000000000000000000000000
χ788-8-4-48-4044-84-2200000011-210-1-12-1−151515−1500−1515000000000000000000000000000000000000000000000
χ798-8-4-48-4044-84-2200000011-210-1-12-115−15−15150015−15000000000000000000000000000000000000000000000
χ808-8-4-4-480444-8-22000000111-20-1-1-12−1515−151515−1500000000000000000000000000000000000000000000000
χ818-8-4-4-480444-8-22000000111-20-1-1-1215−1515−15−151500000000000000000000000000000000000000000000000

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