Finite Group Databasebeta

← Group #14279385

Character table — Group #14279385

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size112222244488888888816161616161616161620202020202040404040404040404040404040484848484880120120240240
order12236664510410121520203030301220206060606060604412121212488882424242424242424840404040122488
χ1111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-11-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111
χ51111111111111111111111111111-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i11111-1-1-1i−i
χ61111111111111111111111111111-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-1-1-111−ii
χ71111111111111111111111111111-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii11111-1-1-1−ii
χ81111111111111111111111111111-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-1-1-111i−i
χ92222222222-222222222-2-2-222-2-2-2-2222222-200000000000000000-20000
χ102222222222-222222222-2-2-222-2-2-2-2-2-2-2-2-2-220000000000000000020000
χ11222-1-1-1-122222-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-122222-1-1-1-1-1-1-1-100000-10000
χ12222-1-1-1-122222-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-12-2-2-2-21111111100000-10000
χ13222-1-1-1-122222-1-122-1-1-1-122-1-1-1-1-1-1-2-21111-22i2i−2i−2i−i−i−i−iiiii0000010000
χ14222-1-1-1-122222-1-122-1-1-1-122-1-1-1-1-1-1-2-21111-2−2i−2i2i2iiiii−i−i−i−i0000010000
χ15222-1-1-1-1222-22-1-122-1-1-11-2-2-1-1111122-1-1-1-1-20000−i3−i3i3i3−i3−i3i3i30000010000
χ16222-1-1-1-1222-22-1-122-1-1-11-2-2-1-1111122-1-1-1-1-20000i3i3−i3−i3i3i3−i3−i30000010000
χ17222-1-1-1-1222-22-1-122-1-1-11-2-2-1-11111-2-211112000033−3−3−3−33300000-10000
χ18222-1-1-1-1222-22-1-122-1-1-11-2-2-1-11111-2-2111120000−3−33333−3−300000-10000
χ1944444444-1-14-14-1-1-1-1-1-14-1-1-1-1-1-1-1-100000000000000000004-1-1-1-100000
χ2044444444-1-14-14-1-1-1-1-1-14-1-1-1-1-1-1-1-10000000000000000000-4111100000
χ2144444444-1-1-4-14-1-1-1-1-1-1-411-1-1111100000000000000000000−5−55500000
χ2244444444-1-1-4-14-1-1-1-1-1-1-411-1-111110000000000000000000055−5−500000
χ234444444-44404-44-4-4444000-4-4000000000000000000000000000000000
χ244444444-4-1-10-1-4-111-1-1-10−5511−5−55500000000000000000000ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ11800000
χ254444444-4-1-10-1-4-111-1-1-10−5511−5−55500000000000000000000−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ11800000
χ264444444-4-1-10-1-4-111-1-1-105−51155−5−500000000000000000000ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ11800000
χ274444444-4-1-10-1-4-111-1-1-105−51155−5−500000000000000000000−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ11800000
χ28444-2-2-2-2-444042-2-4-4-2-2-200022000000−2i32i3−2i32i300000000000000000000000
χ29444-2-2-2-2-444042-2-4-4-2-2-2000220000002i3−2i32i3−2i300000000000000000000000
χ3044-44-4-440440-40400-4-4400000000000000000000000000000000002-200
χ3144-44-4-440440-40400-4-440000000000000000000000000000000000-2200
χ324-40400-404-400040000-40000000002-222-2-202−22−22−22−22−22−20000000000
χ334-40400-404-400040000-40000000002-222-2-20−22−22−22−22−22−220000000000
χ344-40400-404-400040000-4000000000-22-2-2220−i2i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000
χ354-40400-404-400040000-4000000000-22-2-2220i2−i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000
χ364-40-2−2i32i3204-4000-200−2i32i320000000002-2−1−i3−1+i31+i31−i302−22−2−ζ23+ζ29−ζ47+ζ53−ζ71+ζ77+ζ101−ζ119ζ23−ζ29+ζ47−ζ53+ζ71−ζ77−ζ101+ζ119−ζ7+ζ13−ζ31+ζ37+ζ61−ζ79−ζ103+ζ109ζ7−ζ13+ζ31−ζ37−ζ61+ζ79+ζ103−ζ109−ζ23+ζ29−ζ47+ζ53−ζ71+ζ77+ζ101−ζ119ζ23−ζ29+ζ47−ζ53+ζ71−ζ77−ζ101+ζ119−ζ7+ζ13−ζ31+ζ37+ζ61−ζ79−ζ103+ζ109ζ7−ζ13+ζ31−ζ37−ζ61+ζ79+ζ103−ζ1090000000000
χ374-40-2−2i32i3204-4000-200−2i32i320000000002-2−1−i3−1+i31+i31−i30−22−22ζ23−ζ29+ζ47−ζ53+ζ71−ζ77−ζ101+ζ119−ζ23+ζ29−ζ47+ζ53−ζ71+ζ77+ζ101−ζ119ζ7−ζ13+ζ31−ζ37−ζ61+ζ79+ζ103−ζ109−ζ7+ζ13−ζ31+ζ37+ζ61−ζ79−ζ103+ζ109ζ23−ζ29+ζ47−ζ53+ζ71−ζ77−ζ101+ζ119−ζ23+ζ29−ζ47+ζ53−ζ71+ζ77+ζ101−ζ119ζ7−ζ13+ζ31−ζ37−ζ61+ζ79+ζ103−ζ109−ζ7+ζ13−ζ31+ζ37+ζ61−ζ79−ζ103+ζ1090000000000
χ384-40-2−2i32i3204-4000-200−2i32i32000000000-221+i31−i3−1−i3−1+i30−i2i2i2−i2ζ23+ζ29+ζ47+ζ53+ζ71+ζ77+ζ101+ζ119−ζ23−ζ29−ζ47−ζ53−ζ71−ζ77−ζ101−ζ119ζ7+ζ13+ζ31+ζ37+ζ61+ζ79+ζ103+ζ109−ζ7−ζ13−ζ31−ζ37−ζ61−ζ79−ζ103−ζ109−ζ23−ζ29−ζ47−ζ53−ζ71−ζ77−ζ101−ζ119ζ23+ζ29+ζ47+ζ53+ζ71+ζ77+ζ101+ζ119−ζ7−ζ13−ζ31−ζ37−ζ61−ζ79−ζ103−ζ109ζ7+ζ13+ζ31+ζ37+ζ61+ζ79+ζ103+ζ1090000000000
χ394-40-2−2i32i3204-4000-200−2i32i32000000000-221+i31−i3−1−i3−1+i30i2−i2−i2i2−ζ23−ζ29−ζ47−ζ53−ζ71−ζ77−ζ101−ζ119ζ23+ζ29+ζ47+ζ53+ζ71+ζ77+ζ101+ζ119−ζ7−ζ13−ζ31−ζ37−ζ61−ζ79−ζ103−ζ109ζ7+ζ13+ζ31+ζ37+ζ61+ζ79+ζ103+ζ109ζ23+ζ29+ζ47+ζ53+ζ71+ζ77+ζ101+ζ119−ζ23−ζ29−ζ47−ζ53−ζ71−ζ77−ζ101−ζ119ζ7+ζ13+ζ31+ζ37+ζ61+ζ79+ζ103+ζ109−ζ7−ζ13−ζ31−ζ37−ζ61−ζ79−ζ103−ζ1090000000000
χ404-40-22i3−2i3204-4000-2002i3−2i320000000002-2−1+i3−1−i31−i31+i302−22−2−ζ7+ζ13−ζ31+ζ37+ζ61−ζ79−ζ103+ζ109ζ7−ζ13+ζ31−ζ37−ζ61+ζ79+ζ103−ζ109−ζ23+ζ29−ζ47+ζ53−ζ71+ζ77+ζ101−ζ119ζ23−ζ29+ζ47−ζ53+ζ71−ζ77−ζ101+ζ119−ζ7+ζ13−ζ31+ζ37+ζ61−ζ79−ζ103+ζ109ζ7−ζ13+ζ31−ζ37−ζ61+ζ79+ζ103−ζ109−ζ23+ζ29−ζ47+ζ53−ζ71+ζ77+ζ101−ζ119ζ23−ζ29+ζ47−ζ53+ζ71−ζ77−ζ101+ζ1190000000000
χ414-40-22i3−2i3204-4000-2002i3−2i320000000002-2−1+i3−1−i31−i31+i30−22−22ζ7−ζ13+ζ31−ζ37−ζ61+ζ79+ζ103−ζ109−ζ7+ζ13−ζ31+ζ37+ζ61−ζ79−ζ103+ζ109ζ23−ζ29+ζ47−ζ53+ζ71−ζ77−ζ101+ζ119−ζ23+ζ29−ζ47+ζ53−ζ71+ζ77+ζ101−ζ119ζ7−ζ13+ζ31−ζ37−ζ61+ζ79+ζ103−ζ109−ζ7+ζ13−ζ31+ζ37+ζ61−ζ79−ζ103+ζ109ζ23−ζ29+ζ47−ζ53+ζ71−ζ77−ζ101+ζ119−ζ23+ζ29−ζ47+ζ53−ζ71+ζ77+ζ101−ζ1190000000000
χ424-40-22i3−2i3204-4000-2002i3−2i32000000000-221−i31+i3−1+i3−1−i30−i2i2i2−i2ζ7+ζ13+ζ31+ζ37+ζ61+ζ79+ζ103+ζ109−ζ7−ζ13−ζ31−ζ37−ζ61−ζ79−ζ103−ζ109ζ23+ζ29+ζ47+ζ53+ζ71+ζ77+ζ101+ζ119−ζ23−ζ29−ζ47−ζ53−ζ71−ζ77−ζ101−ζ119−ζ7−ζ13−ζ31−ζ37−ζ61−ζ79−ζ103−ζ109ζ7+ζ13+ζ31+ζ37+ζ61+ζ79+ζ103+ζ109−ζ23−ζ29−ζ47−ζ53−ζ71−ζ77−ζ101−ζ119ζ23+ζ29+ζ47+ζ53+ζ71+ζ77+ζ101+ζ1190000000000
χ434-40-22i3−2i3204-4000-2002i3−2i32000000000-221−i31+i3−1+i3−1−i30i2−i2−i2i2−ζ7−ζ13−ζ31−ζ37−ζ61−ζ79−ζ103−ζ109ζ7+ζ13+ζ31+ζ37+ζ61+ζ79+ζ103+ζ109−ζ23−ζ29−ζ47−ζ53−ζ71−ζ77−ζ101−ζ119ζ23+ζ29+ζ47+ζ53+ζ71+ζ77+ζ101+ζ119ζ7+ζ13+ζ31+ζ37+ζ61+ζ79+ζ103+ζ109−ζ7−ζ13−ζ31−ζ37−ζ61−ζ79−ζ103−ζ109ζ23+ζ29+ζ47+ζ53+ζ71+ζ77+ζ101+ζ119−ζ23−ζ29−ζ47−ζ53−ζ71−ζ77−ζ101−ζ1190000000000
χ44888-4-4-4-48-2-28-2-41-2-2111-4-2-211111100000000000000000000000000000
χ45888-4-4-4-48-2-2-8-2-41-2-211142211-1-1-1-100000000000000000000000000000
χ46888-4-4-4-4-8-2-20-241221110−2525-1-155−5−500000000000000000000000000000
χ47888-4-4-4-4-8-2-20-24122111025−25-1-1−5−55500000000000000000000000000000
χ4888-88-8-880-2-2020-2−252522-2000−2525000000000000000000000000000000000
χ4988-88-8-880-2-2020-225−2522-200025−25000000000000000000000000000000000
χ5088-8-444-40880-80-40044-400000000000000000000000000000000000000
χ5188-8-444-40-2-20201−2525-1-110005−5−ζ4+ζ28+ζ44−ζ52−ζ68+ζ76+ζ92−ζ116ζ4−ζ28−ζ44+ζ52+ζ68−ζ76−ζ92+ζ116ζ4+ζ28−ζ44−ζ52−ζ68−ζ76+ζ92+ζ116−ζ4−ζ28+ζ44+ζ52+ζ68+ζ76−ζ92−ζ11600000000000000000000000000000
χ5288-8-444-40-2-20201−2525-1-110005−5ζ4−ζ28−ζ44+ζ52+ζ68−ζ76−ζ92+ζ116−ζ4+ζ28+ζ44−ζ52−ζ68+ζ76+ζ92−ζ116−ζ4−ζ28+ζ44+ζ52+ζ68+ζ76−ζ92−ζ116ζ4+ζ28−ζ44−ζ52−ζ68−ζ76+ζ92+ζ11600000000000000000000000000000
χ5388-8-444-40-2-2020125−25-1-11000−55ζ4+ζ28−ζ44−ζ52−ζ68−ζ76+ζ92+ζ116−ζ4−ζ28+ζ44+ζ52+ζ68+ζ76−ζ92−ζ116ζ4−ζ28−ζ44+ζ52+ζ68−ζ76−ζ92+ζ116−ζ4+ζ28+ζ44−ζ52−ζ68+ζ76+ζ92−ζ11600000000000000000000000000000
χ5488-8-444-40-2-2020125−25-1-11000−55−ζ4−ζ28+ζ44+ζ52+ζ68+ζ76−ζ92−ζ116ζ4+ζ28−ζ44−ζ52−ζ68−ζ76+ζ92+ζ116−ζ4+ζ28+ζ44−ζ52−ζ68+ζ76+ζ92−ζ116ζ4−ζ28−ζ44+ζ52+ζ68−ζ76−ζ92+ζ11600000000000000000000000000000
χ5516-1601600-160-44000-40000400000000000000000000000000000000000000
χ5616-160-8−8i38i380-440002002i3−2i3-200000000000000000000000000000000000000
χ5716-160-88i3−8i380-44000200−2i32i3-200000000000000000000000000000000000000

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