Finite Group Databasebeta

← Group #13088701

Character table — Group #13088701

Order 1440.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1122222444444444444556688888888888888810101010101212202020202020242424242424303030303030454545456060606060609090
order123346635610121212121515303044441515152030303060606060606060602121212121212666612122020606060602288888888662424242488
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
χ91111-1111111-1-1-1-11111111-1111-1111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1111-111-1-11-11-11-111111-11-11-1-1-1
χ101111-1111111-1-1-1-11111111-1111-1111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1111-111-1-11-1-11-11-1-1-1-11-1-11-1111
χ111111-1111111-1-1-1-1111111-11111-1111-1-1-1-1-1-1-1-1-11111-11-1-1-1-111-11-1-111-111-11-1-1-1-1-1-111-11-111
χ121111-1111111-1-1-1-1111111-11111-1111-1-1-1-1-1-1-1-1-11111-11-1-1-1-111-11-1-111-11-11-111111-11-11-11-1-1
χ131111-1111111-1-1-1-11111-1-11-1111-1111-1-1-1-1-1-1-1-11-1-1-1-11-11111-1-11-111-1-1-11i−i−iiii−i−i-11i−i−ii−ii
χ141111-1111111-1-1-1-11111-1-11-1111-1111-1-1-1-1-1-1-1-11-1-1-1-11-11111-1-11-111-1-1-11−iii−i−i−iii-11−iii−ii−i
χ151111-1111111-1-1-1-11111-1-1-11111-1111-1-1-1-1-1-1-1-11-1-1-1-1-111111-1-1-11-1-1111-1i−i−ii−i−iii1-1i−i−iii−i
χ161111-1111111-1-1-1-11111-1-1-11111-1111-1-1-1-1-1-1-1-11-1-1-1-1-111111-1-1-11-1-1111-1−iii−iii−i−i1-1−iii−i−ii
χ17222-122-1-12-122-1-1-1-1-1-1-122222-1-122-1-1-1-122-1-1-1-12-1-122-1-12-1-1-1-1-122-1-1-1-12200000000-1-1000000
χ18222-122-1-12-122-1-1-1-1-1-1-122-2-22-1-122-1-1-1-122-1-1-1-12-1-122112-1-1-1-1-1-2-21111-2-20000000011000000
χ19222-122-1-12-122-1-1-1-1-1-1-1-2-2222-1-122-1-1-1-122-1-1-1-1-211-2-2-1-1-21111122-1-1-1-1-2-20000000011000000
χ20222-122-1-12-122-1-1-1-1-1-1-1-2-2-2-22-1-122-1-1-1-122-1-1-1-1-211-2-211-211111-2-211112200000000-1-1000000
χ21222-1-22-1-12-12-2111-1-1-1-1222-22-1-1-22-1-111-2-21111-2-1-122-11-2111-1-12-2-1-1112-200000000-11000000
χ22222-1-22-1-12-12-2111-1-1-1-122-222-1-1-22-1-111-2-21111-2-1-1221-1-2111-1-1-2211-1-1-22000000001-1000000
χ23222-1-22-1-12-12-2111-1-1-1-1-2-22-22-1-1-22-1-111-2-21111211-2-2-112-1-1-1112-2-1-111-22000000001-1000000
χ24222-1-22-1-12-12-2111-1-1-1-1-2-2-222-1-1-22-1-111-2-21111211-2-21-12-1-1-111-2211-1-12-200000000-11000000
χ2522-122-12-12-12-12-1-122222200-1-1-12-1-1-122-1-1-1-1-1-1222-1-100-12-1-1-1-1000000002222000000-1-1-1-100
χ2622-122-12-12-12-12-1-122222200-1-1-12-1-1-122-1-1-1-1-1-1222-1-100-12-1-1-1-100000000-2-2-2-2000000111100
χ2722-122-12-12-12-12-1-12222-2-200-1-1-12-1-1-122-1-1-1-1-1-1-2-2-211001-21111000000002i2i−2i−2i000000−i−iii00
χ2822-122-12-12-12-12-1-12222-2-200-1-1-12-1-1-122-1-1-1-1-1-1-2-2-211001-2111100000000−2i−2i2i2i000000ii−i−i00
χ2922-12-2-12-12-121-21122222200-1-1-1-2-1-1-1-2-2111111-222-1-1001-211-1-1000000002-22-2000000-11-1100
χ3022-12-2-12-12-121-21122222200-1-1-1-2-1-1-1-2-2111111-222-1-1001-211-1-100000000-22-220000001-11-100
χ3122-12-2-12-12-121-2112222-2-200-1-1-1-2-1-1-1-2-21111112-2-21100-12-1-111000000002i−2i−2i2i000000−iii−i00
χ3222-12-2-12-12-121-2112222-2-200-1-1-1-2-1-1-1-2-21111112-2-21100-12-1-11100000000−2i2i2i−2i000000i−i−ii00
χ332-2220-2-222-2-2000022-2-22i−2i002220-2-2-20000000002i−2i2i−2i0000002i−2i000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900000000
χ342-2220-2-222-2-2000022-2-22i−2i002220-2-2-20000000002i−2i2i−2i0000002i−2i0000000000002ζ13+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
χ352-2220-2-222-2-2000022-2-2−2i2i002220-2-2-2000000000−2i2i−2i2i000000−2i2i0000000000002ζ7+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
χ362-2220-2-222-2-2000022-2-2−2i2i002220-2-2-2000000000−2i2i−2i2i000000−2i2i000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900000000
χ3744444444-14-14444-1-1-1-10044-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000044000000-1-1-1-1-1-1000000000000000000
χ3844444444-14-14444-1-1-1-100-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000-4-4000000111111000000000000000000
χ394444-4444-14-1-4-4-4-4-1-1-1-1004-4-1-1-11-1-1-111111111000004-4000000-11-1-111000000000000000000
χ404444-4444-14-1-4-4-4-4-1-1-1-100-44-1-1-11-1-1-11111111100000-440000001-111-1-1000000000000000000
χ41444-244-2-2-1-2-14-2-2-21−i1521+i1521−i1521+i1520044-11−i1521+i152-1-11−i1521+i1521−i1521+i152-1-11−i1521−i1521+i1521+i15200000-2-2000000-1-11−i1521+i1521−i1521+i152000000000000000000
χ42444-244-2-2-1-2-14-2-2-21−i1521+i1521−i1521+i15200-4-4-11−i1521+i152-1-11−i1521+i1521−i1521+i152-1-11−i1521−i1521+i1521+i152000002200000011−1+i152−1−i152−1+i152−1−i152000000000000000000
χ43444-244-2-2-1-2-14-2-2-21+i1521−i1521+i1521−i1520044-11+i1521−i152-1-11+i1521−i1521+i1521−i152-1-11+i1521+i1521−i1521−i15200000-2-2000000-1-11+i1521−i1521+i1521−i152000000000000000000
χ44444-244-2-2-1-2-14-2-2-21+i1521−i1521+i1521−i15200-4-4-11+i1521−i152-1-11+i1521−i1521+i1521−i152-1-11+i1521+i1521−i1521−i152000002200000011−1−i152−1+i152−1−i152−1+i152000000000000000000
χ45444-2-44-2-2-1-2-1-42221−i1521+i1521−i1521+i152004-4-11−i1521+i1521-11−i1521+i152−1+i152−1−i15211−1+i152−1+i152−1−i152−1−i15200000-22000000-111−i1521+i152−1+i152−1−i152000000000000000000
χ46444-2-44-2-2-1-2-1-42221−i1521+i1521−i1521+i15200-44-11−i1521+i1521-11−i1521+i152−1+i152−1−i15211−1+i152−1+i152−1−i152−1−i152000002-20000001-1−1+i152−1−i1521−i1521+i152000000000000000000
χ47444-2-44-2-2-1-2-1-42221+i1521−i1521+i1521−i152004-4-11+i1521−i1521-11+i1521−i152−1−i152−1+i15211−1−i152−1−i152−1+i152−1+i15200000-22000000-111+i1521−i152−1−i152−1+i152000000000000000000
χ48444-2-44-2-2-1-2-1-42221+i1521−i1521+i1521−i15200-44-11+i1521−i1521-11+i1521−i152−1−i152−1+i15211−1−i152−1−i152−1+i152−1+i152000002-20000001-1−1−i152−1+i1521+i1521−i152000000000000000000
χ4944-2-24-2-21414-2-211-2-2-2-24400-2114-211-2-2-2-211114-2-2-2-200-2-21111000000000000000000000000
χ5044-2-24-2-21414-2-211-2-2-2-2-4-400-2114-211-2-2-2-21111-422220022-1-1-1-1000000000000000000000000
χ5144-2-2-4-2-2141422-1-1-2-2-2-24400-211-4-2112222-1-1-1-1-4-2-2-2-20022-1-111000000000000000000000000
χ5244-2-2-4-2-2141422-1-1-2-2-2-2-4-400-211-4-2112222-1-1-1-14222200-2-211-1-1000000000000000000000000
χ534-44-20-42-242-40000-2-2224i−4i004-2-20-422000000000−2i2i4i−4i000000−2i2i000000000000000000000000
χ544-44-20-42-242-40000-2-222−4i4i004-2-20-4220000000002i−2i−4i4i0000002i−2i000000000000000000000000
χ554-4-2402-4-242-4000044-4-44i−4i00-2-2-202220000000004i−4i−2i2i000000−2i2i000000000000000000000000
χ564-4-2402-4-242-4000044-4-4−4i4i00-2-2-20222000000000−4i4i2i−2i0000002i−2i000000000000000000000000
χ574-4-2-202214-1-4003i−3i-2-2224i−4i00-21102-1-100003i−3i3i−3i0−2i2i−2i2i00003-3i−i000000000000000000000000
χ584-4-2-202214-1-4003i−3i-2-222−4i4i00-21102-1-100003i−3i3i−3i02i−2i2i−2i0000-33−ii000000000000000000000000
χ594-4-2-202214-1-400−3i3i-2-2224i−4i00-21102-1-10000−3i3i−3i3i0−2i2i−2i2i0000-33i−i000000000000000000000000
χ604-4-2-202214-1-400−3i3i-2-222−4i4i00-21102-1-10000−3i3i−3i3i02i−2i2i−2i00003-3−ii000000000000000000000000
χ6188-488-48-4-2-4-2-48-4-4-2-2-2-20000111-2111-2-21111110000000000000000000000000000000000000
χ6288-48-8-48-4-2-4-24-844-2-2-2-20000111211122-1-1-1-1-1-10000000000000000000000000000000000000
χ6388-4-48-4-42-22-2-4-4221−i151+i151−i151+i1500001−1+i152−1−i152-21−1+i152−1−i1521−i151+i1511−1+i152−1+i152−1−i152−1−i1520000000000000000000000000000000000000
χ6488-4-48-4-42-22-2-4-4221+i151−i151+i151−i1500001−1−i152−1+i152-21−1−i152−1+i1521+i151−i1511−1−i152−1−i152−1+i152−1+i1520000000000000000000000000000000000000
χ6588-4-4-8-4-42-22-244-2-21−i151+i151−i151+i1500001−1+i152−1−i15221−1+i152−1−i152−1+i15−1−i15-1-11−i1521−i1521+i1521+i1520000000000000000000000000000000000000
χ6688-4-4-8-4-42-22-244-2-21+i151−i151+i151−i1500001−1−i152−1+i15221−1−i152−1+i152−1−i15−1+i15-1-11+i1521+i1521−i1521−i1520000000000000000000000000000000000000
χ678-8880-8-88-2-820000-2-2220000-2-2-20222000000000000000000000000000000000000000000000
χ688-88-40-84-4-24200001−i151+i15−1+i15−1−i150000-21−i151+i1502−1+i15−1−i15000000000000000000000000000000000000000000000
χ698-88-40-84-4-24200001+i151−i15−1−i15−1+i150000-21+i151−i1502−1−i15−1+i15000000000000000000000000000000000000000000000
χ708-8-4804-8-4-2420000-2-22200001110-1-1-100−1515−151515−150000000000000000000000000000000000000
χ718-8-4804-8-4-2420000-2-22200001110-1-1-10015−1515−15−15150000000000000000000000000000000000000
χ728-8-4-40442-2-22006i−6i1−i151+i15−1+i15−1−i1500001−1+i152−1−i1520-11−i1521+i15200−1515−ζ14−ζ22−2ζ38−2ζ46−2ζ62−ζ86−2ζ94−ζ118ζ14+ζ22+2ζ38+2ζ46+2ζ62+ζ86+2ζ94+ζ118−2ζ14−2ζ22−ζ38−ζ46−ζ62−2ζ86−ζ94−2ζ1182ζ14+2ζ22+ζ38+ζ46+ζ62+2ζ86+ζ94+2ζ1180000000000000000000000000000000000000
χ738-8-4-40442-2-22006i−6i1+i151−i15−1−i15−1+i1500001−1−i152−1+i1520-11+i1521−i1520015−15−2ζ14−2ζ22−ζ38−ζ46−ζ62−2ζ86−ζ94−2ζ1182ζ14+2ζ22+ζ38+ζ46+ζ62+2ζ86+ζ94+2ζ118−ζ14−ζ22−2ζ38−2ζ46−2ζ62−ζ86−2ζ94−ζ118ζ14+ζ22+2ζ38+2ζ46+2ζ62+ζ86+2ζ94+ζ1180000000000000000000000000000000000000
χ748-8-4-40442-2-2200−6i6i1−i151+i15−1+i15−1−i1500001−1+i152−1−i1520-11−i1521+i1520015−15ζ14+ζ22+2ζ38+2ζ46+2ζ62+ζ86+2ζ94+ζ118−ζ14−ζ22−2ζ38−2ζ46−2ζ62−ζ86−2ζ94−ζ1182ζ14+2ζ22+ζ38+ζ46+ζ62+2ζ86+ζ94+2ζ118−2ζ14−2ζ22−ζ38−ζ46−ζ62−2ζ86−ζ94−2ζ1180000000000000000000000000000000000000
χ758-8-4-40442-2-2200−6i6i1+i151−i15−1−i15−1+i1500001−1−i152−1+i1520-11+i1521−i15200−15152ζ14+2ζ22+ζ38+ζ46+ζ62+2ζ86+ζ94+2ζ118−2ζ14−2ζ22−ζ38−ζ46−ζ62−2ζ86−ζ94−2ζ118ζ14+ζ22+2ζ38+2ζ46+2ζ62+ζ86+2ζ94+ζ118−ζ14−ζ22−2ζ38−2ζ46−2ζ62−ζ86−2ζ94−ζ1180000000000000000000000000000000000000

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