Finite Group Databasebeta

← Group #13088714

Character table — Group #13088714

Order 1440.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1122222444444444444556688888888888888810101010101212202020202020242424242424303030303030454545456060606060609090
order122336635666661015153030442410151515303030303030303030303041212121261212121212121210203030606024888888886122424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111-1-111111111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ4111111111111111111111-1-111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ51111111111111111111-1-111111111111111111-1-1-1-1-111-1-1-1-1-1-1111111-1-1ii−i−iii−i−i-1-1ii−i−ii−i
χ61111111111111111111-1-111111111111111111-1-1-1-1-111-1-1-1-1-1-1111111-1-1−i−iii−i−iii-1-1−i−iii−ii
χ71111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii11ii−i−i−ii
χ81111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i11−i−iiii−i
χ911-1111111-1-1-1-1111111111-1-1111-1-1111-1-1-1-1-1-1-111111-1-1-111-1-11-111-1-1-111-11-11111-111-11-1-1-1
χ1011-1111111-1-1-1-1111111111-1-1111-1-1111-1-1-1-1-1-1-111111-1-1-111-1-11-111-1-1-11-11-11-1-1-1-1-11-11-1111
χ1111-1111111-1-1-1-111111111-11-1111-1-1111-1-1-1-1-1-1-11111-11-1-111-1-1-11-1-1111-11-11-1-1-1-1-11-11-11-111
χ1211-1111111-1-1-1-111111111-11-1111-1-1111-1-1-1-1-1-1-11111-11-1-111-1-1-11-1-1111-1-11-1111111-1-11-11-1-1
χ1311-1111111-1-1-1-1111111-1-11-1-1111-1-1111-1-1-1-1-1-11-1-1-1-11-111-1-1111-111-1-11-1i−i−iiii−i−i1-1i−i−ii−ii
χ1411-1111111-1-1-1-1111111-1-11-1-1111-1-1111-1-1-1-1-1-11-1-1-1-11-111-1-1111-111-1-11-1−iii−i−i−iii1-1−iii−ii−i
χ1511-1111111-1-1-1-1111111-1-1-11-1111-1-1111-1-1-1-1-1-11-1-1-1-1-1111-1-111-11-1-111-11i−i−ii−i−iii-11i−i−iii−i
χ1611-1111111-1-1-1-1111111-1-1-11-1111-1-1111-1-1-1-1-1-11-1-1-1-1-1111-1-111-11-1-111-11−iii−iii−i−i-11−iii−i−ii
χ172222-12-1-122-1-1-1-12-1-1-1-1222222-1-1-1-12-1-122-1-1-1-12-1-122-1-12-1-1-1-1-122-1-1-1-12200000000-1-1000000
χ182222-12-1-122-1-1-1-12-1-1-1-122-2-222-1-1-1-12-1-122-1-1-1-12-1-122112-1-1-1-1-1-2-21111-2-20000000011000000
χ192222-12-1-122-1-1-1-12-1-1-1-1-2-22222-1-1-1-12-1-122-1-1-1-1-211-2-2-1-1-21111122-1-1-1-1-2-20000000011000000
χ202222-12-1-122-1-1-1-12-1-1-1-1-2-2-2-222-1-1-1-12-1-122-1-1-1-1-211-2-211-211111-2-211112200000000-1-1000000
χ21222-12-12-12-12-1-1-12222222002-1-1-122-1-1-1-1-1-1-1-1-1222-1-100-12-1-1-1-1000000002222000000-1-1-1-100
χ22222-12-12-12-12-1-1-12222222002-1-1-122-1-1-1-1-1-1-1-1-1222-1-100-12-1-1-1-100000000-2-2-2-2000000111100
χ23222-12-12-12-12-1-1-122222-2-2002-1-1-122-1-1-1-1-1-1-1-1-1-2-2-211001-21111000000002i2i−2i−2i000000−i−iii00
χ24222-12-12-12-12-1-1-122222-2-2002-1-1-122-1-1-1-1-1-1-1-1-1-2-2-211001-2111100000000−2i−2i2i2i000000ii−i−i00
χ2522-22-12-1-12-2111-12-1-1-1-1222-2-22-1-1112-1-1-2-21111-2-1-122-11-21-1-1112-2-1-111-22000000001-1000000
χ2622-22-12-1-12-2111-12-1-1-1-122-22-22-1-1112-1-1-2-21111-2-1-1221-1-21-1-111-2211-1-12-200000000-11000000
χ2722-22-12-1-12-2111-12-1-1-1-1-2-22-2-22-1-1112-1-1-2-21111211-2-2-112-111-1-12-2-1-1112-200000000-11000000
χ2822-22-12-1-12-2111-12-1-1-1-1-2-2-22-22-1-1112-1-1-2-21111211-2-21-12-111-1-1-2211-1-1-22000000001-1000000
χ2922-2-12-12-121-211-1222222200-2-1-1-1-2-2-1-1-1111111-222-1-1001-2-1-111000000002-22-2000000-11-1100
χ3022-2-12-12-121-211-1222222200-2-1-1-1-2-2-1-1-1111111-222-1-1001-2-1-11100000000-22-220000001-11-100
χ3122-2-12-12-121-211-122222-2-200-2-1-1-1-2-2-1-1-11111112-2-21100-1211-1-1000000002i−2i−2i2i000000−iii−i00
χ3222-2-12-12-121-211-122222-2-200-2-1-1-1-2-2-1-1-11111112-2-21100-1211-1-100000000−2i2i2i−2i000000i−i−ii00
χ332-2022-2-2220000-2-222-2-22i−2i00022200-2-2-200000002i−2i2i−2i00002i−2i000000000000002ζ7+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
χ342-2022-2-2220000-2-222-2-22i−2i00022200-2-2-200000002i−2i2i−2i00002i−2i00000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900000000
χ352-2022-2-2220000-2-222-2-2−2i2i00022200-2-2-20000000−2i2i−2i2i0000−2i2i00000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900000000
χ362-2022-2-2220000-2-222-2-2−2i2i00022200-2-2-20000000−2i2i−2i2i0000−2i2i000000000000002ζ13+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
χ3744444444-144444-1-1-1-1-10044-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000044000000-1-1-1-1-1-1000000000000000000
χ3844444444-144444-1-1-1-1-100-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000-4-4000000111111000000000000000000
χ394444-24-2-2-14-2-2-2-2-11−i1521+i1521−i1521+i1520044-1-11−i1521+i1521−i1521+i152-11−i1521+i152-1-11−i1521−i1521+i1521+i15200000-2-2000000-1-11−i1521+i1521−i1521+i152000000000000000000
χ404444-24-2-2-14-2-2-2-2-11−i1521+i1521−i1521+i15200-4-4-1-11−i1521+i1521−i1521+i152-11−i1521+i152-1-11−i1521−i1521+i1521+i152000002200000011−1+i152−1−i152−1+i152−1−i152000000000000000000
χ414444-24-2-2-14-2-2-2-2-11+i1521−i1521+i1521−i1520044-1-11+i1521−i1521+i1521−i152-11+i1521−i152-1-11+i1521+i1521−i1521−i15200000-2-2000000-1-11+i1521−i1521+i1521−i152000000000000000000
χ424444-24-2-2-14-2-2-2-2-11+i1521−i1521+i1521−i15200-4-4-1-11+i1521−i1521+i1521−i152-11+i1521−i152-1-11+i1521+i1521−i1521−i152000002200000011−1−i152−1+i152−1−i152−1+i152000000000000000000
χ43444-2-2-2-214-2-21114-2-2-2-244004-211-2-2-211-2-211114-2-2-2-200-2-21111000000000000000000000000
χ44444-2-2-2-214-2-21114-2-2-2-2-4-4004-211-2-2-211-2-21111-422220022-1-1-1-1000000000000000000000000
χ4544-444444-1-4-4-4-44-1-1-1-1-1004-41-1-1-111-1-1-1111111000004-4000000-11-1-111000000000000000000
χ4644-444444-1-4-4-4-44-1-1-1-1-100-441-1-1-111-1-1-111111100000-440000001-111-1-1000000000000000000
χ4744-44-24-2-2-1-4222-2-11−i1521+i1521−i1521+i152004-41-11−i1521+i152−1+i152−1−i152-11−i1521+i15211−1+i152−1+i152−1−i152−1−i15200000-22000000-111−i1521+i152−1+i152−1−i152000000000000000000
χ4844-44-24-2-2-1-4222-2-11−i1521+i1521−i1521+i15200-441-11−i1521+i152−1+i152−1−i152-11−i1521+i15211−1+i152−1+i152−1−i152−1−i152000002-20000001-1−1+i152−1−i1521−i1521+i152000000000000000000
χ4944-44-24-2-2-1-4222-2-11+i1521−i1521+i1521−i152004-41-11+i1521−i152−1−i152−1+i152-11+i1521−i15211−1−i152−1−i152−1+i152−1+i15200000-22000000-111+i1521−i152−1−i152−1+i152000000000000000000
χ5044-44-24-2-2-1-4222-2-11+i1521−i1521+i1521−i15200-441-11+i1521−i152−1−i152−1+i152-11+i1521−i15211−1−i152−1−i152−1+i152−1+i152000002-20000001-1−1−i152−1+i1521+i1521−i152000000000000000000
χ5144-4-2-2-2-21422-1-114-2-2-2-24400-4-21122-21122-1-1-1-1-4-2-2-2-2002211-1-1000000000000000000000000
χ5244-4-2-2-2-21422-1-114-2-2-2-2-4-400-4-21122-21122-1-1-1-14222200-2-2-1-111000000000000000000000000
χ534-404-2-42-2400002-4-2-2224i−4i0004-2-200-4220000000−2i2i4i−4i0000−2i2i00000000000000000000000000
χ544-404-2-42-2400002-4-2-222−4i4i0004-2-200-42200000002i−2i−4i4i00002i−2i00000000000000000000000000
χ554-40-242-4-2400002-444-4-44i−4i000-2-2-20022200000004i−4i−2i2i0000−2i2i00000000000000000000000000
χ564-40-242-4-2400002-444-4-4−4i4i000-2-2-2002220000000−4i4i2i−2i00002i−2i00000000000000000000000000
χ574-40-2-22214003-3-1-4-2-2224i−4i000-211002-1-1003-33-30−2i2i−2i2i0000i−i3i−3i000000000000000000000000
χ584-40-2-22214003-3-1-4-2-222−4i4i000-211002-1-1003-33-302i−2i2i−2i0000−ii−3i3i000000000000000000000000
χ594-40-2-2221400-33-1-4-2-2224i−4i000-211002-1-100-33-330−2i2i−2i2i0000i−i−3i3i000000000000000000000000
χ604-40-2-2221400-33-1-4-2-222−4i4i000-211002-1-100-33-3302i−2i2i−2i0000−ii3i−3i000000000000000000000000
χ61888-48-48-4-2-48-4-4-4-2-2-2-2-20000-2111-2-21111111110000000000000000000000000000000000000
χ62888-4-4-4-42-2-4-4222-21−i151+i151−i151+i150000-21−1+i152−1−i1521−i151+i151−1+i152−1−i15211−1+i152−1+i152−1−i152−1−i1520000000000000000000000000000000000000
χ63888-4-4-4-42-2-4-4222-21+i151−i151+i151−i150000-21−1−i152−1+i1521+i151−i151−1−i152−1+i15211−1−i152−1−i152−1+i152−1+i1520000000000000000000000000000000000000
χ6488-8-48-48-4-24-844-4-2-2-2-2-20000211122111-1-1-1-1-1-10000000000000000000000000000000000000
χ6588-8-4-4-4-42-244-2-22-21−i151+i151−i151+i15000021−1+i152−1−i152−1+i15−1−i151−1+i152−1−i152-1-11−i1521−i1521+i1521+i1520000000000000000000000000000000000000
χ6688-8-4-4-4-42-244-2-22-21+i151−i151+i151−i15000021−1−i152−1+i152−1−i15−1+i151−1−i152−1+i152-1-11+i1521+i1521−i1521−i1520000000000000000000000000000000000000
χ678-8088-8-88-20000-82-2-22200000-2-2-2002220000000000000000000000000000000000000000000
χ688-808-4-84-4-20000421−i151+i15−1+i15−1−i1500000-21−i151+i15002−1+i15−1−i150000000000000000000000000000000000000000000
χ698-808-4-84-4-20000421+i151−i15−1−i15−1+i1500000-21+i151−i15002−1−i15−1+i150000000000000000000000000000000000000000000
χ708-80-484-8-4-2000042-2-2220000011100-1-1-1−i15i15−i15i15i15−i150000000000000000000000000000000000000
χ718-80-484-8-4-2000042-2-2220000011100-1-1-1i15−i15i15−i15−i15i150000000000000000000000000000000000000
χ728-80-4-4442-2006-6-221−i151+i15−1+i15−1−i15000001−1+i152−1−i15200-11−i1521+i152i15−i15−3−i1523+i152−3+i1523−i1520000000000000000000000000000000000000
χ738-80-4-4442-2006-6-221+i151−i15−1−i15−1+i15000001−1−i152−1+i15200-11+i1521−i152−i15i15−3+i1523−i152−3−i1523+i1520000000000000000000000000000000000000
χ748-80-4-4442-200-66-221−i151+i15−1+i15−1−i15000001−1+i152−1−i15200-11−i1521+i152−i15i153+i152−3−i1523−i152−3+i1520000000000000000000000000000000000000
χ758-80-4-4442-200-66-221+i151−i15−1−i15−1+i15000001−1−i152−1+i15200-11+i1521−i152i15−i153−i152−3+i1523+i152−3−i1520000000000000000000000000000000000000

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