Finite Group Databasebeta

← Group #14512415

Character table — Group #14512415

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11244556688888101010101024242424303032323232404040404040404040404040484848486060120120120120120120
order12451022243612122048888481020241530606066121224242424242424242020404088444888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1
χ3111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-11-1-11-1-1
χ4111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111
χ511111-1-11111111-1ii−i−i1111-1-11111-1-1-1-1iiii−i−i−i−i1111i−i-1i−i-1i−i
χ611111-1-11111111-1ii−i−i-1-111-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-1i−i1−ii1−ii
χ711111-1-11111111-1−i−iii1111-1-11111-1-1-1-1−i−i−i−iiiii1111−ii-1−ii-1−ii
χ811111-1-11111111-1−i−iii-1-111-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-1−ii1i−i1i−i
χ9222222222-1-1-1-1222222002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022000000
χ10222222222-1-1-1-122-2-2-2-2002222-1-1-1-1-1-1-1-1111111110000-2-2000000
χ1122222-2-222-1-1-1-12-22i2i−2i−2i0022-2-2-1-1-1-11111−i−i−i−iiiii00002i−2i000000
χ1222222-2-222-1-1-1-12-2−2i−2i2i2i0022-2-2-1-1-1-11111iiii−i−i−i−i0000−2i2i000000
χ1322-22222-2222-2-2-2-2000000-22-2222-2-222-2-200000000000000000000
χ1422-22222-22-1-111-2-2000000-22-22-1-111-1-11133−3−333−3−3000000000000
χ1522-22222-22-1-111-2-2000000-22-22-1-111-1-111−3−333−3−333000000000000
χ1622-222-2-2-2222-2-2-22000000-222-222-2-2-2-22200000000000000000000
χ1722-222-2-2-22-1-111-22000000-222-2-1-11111-1-1−i3−i3i3i3i3i3−i3−i3000000000000
χ1822-222-2-2-22-1-111-22000000-222-2-1-11111-1-1i3i3−i3−i3−i3−i3i3i3000000000000
χ193333333-1-100003333331-1-1-1-1-1000000000000000011-1-1-1-1111-1-1-1
χ203333333-1-10000333333-11-1-1-1-10000000000000000-1-111-1-1-1-1-1111
χ213333333-1-1000033-3-3-3-31-1-1-1-1-1000000000000000011-1-1111-1-1-111
χ223333333-1-1000033-3-3-3-3-11-1-1-1-10000000000000000-1-11111-1111-1-1
χ2333333-3-3-1-100003-33i3i−3i−3i1-1-1-111000000000000000011-1-1−ii-1i−i1−ii
χ2433333-3-3-1-100003-33i3i−3i−3i-11-1-1110000000000000000-1-111−ii1−ii-1i−i
χ2533333-3-3-1-100003-3−3i−3i3i3i1-1-1-111000000000000000011-1-1i−i-1−ii1i−i
χ2633333-3-3-1-100003-3−3i−3i3i3i-11-1-1110000000000000000-1-111i−i1i−i-1−ii
χ27444-1-100444444-10000044-1-100-1-1-1-1000000000000-1-1-1-100000000
χ28444-1-100444444-100000-4-4-1-100-1-1-1-1000000000000111100000000
χ2944-4-1-100-4444-4-4100000001-100-1-111000000000000−55−5500000000
χ3044-4-1-100-4444-4-4100000001-100-1-1110000000000005−55−500000000
χ314-404-44-4001-13−30022−2222−220000001-13−31-13−3ζ7−ζ29+ζ31−ζ53−ζ77+ζ79−ζ101+ζ103−ζ7+ζ29−ζ31+ζ53+ζ77−ζ79+ζ101−ζ103ζ13−ζ23+ζ37−ζ47+ζ61−ζ71+ζ109−ζ119−ζ13+ζ23−ζ37+ζ47−ζ61+ζ71−ζ109+ζ119ζ7−ζ29+ζ31−ζ53−ζ77+ζ79−ζ101+ζ103−ζ7+ζ29−ζ31+ζ53+ζ77−ζ79+ζ101−ζ103ζ13−ζ23+ζ37−ζ47+ζ61−ζ71+ζ109−ζ119−ζ13+ζ23−ζ37+ζ47−ζ61+ζ71−ζ109+ζ119000000000000
χ324-404-44-4001-13−300−2222−22220000001-13−31-13−3−ζ7+ζ29−ζ31+ζ53+ζ77−ζ79+ζ101−ζ103ζ7−ζ29+ζ31−ζ53−ζ77+ζ79−ζ101+ζ103−ζ13+ζ23−ζ37+ζ47−ζ61+ζ71−ζ109+ζ119ζ13−ζ23+ζ37−ζ47+ζ61−ζ71+ζ109−ζ119−ζ7+ζ29−ζ31+ζ53+ζ77−ζ79+ζ101−ζ103ζ7−ζ29+ζ31−ζ53−ζ77+ζ79−ζ101+ζ103−ζ13+ζ23−ζ37+ζ47−ζ61+ζ71−ζ109+ζ119ζ13−ζ23+ζ37−ζ47+ζ61−ζ71+ζ109−ζ119000000000000
χ334-404-44-4001-1−330022−2222−220000001-1−331-1−33−ζ13+ζ23−ζ37+ζ47−ζ61+ζ71−ζ109+ζ119ζ13−ζ23+ζ37−ζ47+ζ61−ζ71+ζ109−ζ119−ζ7+ζ29−ζ31+ζ53+ζ77−ζ79+ζ101−ζ103ζ7−ζ29+ζ31−ζ53−ζ77+ζ79−ζ101+ζ103−ζ13+ζ23−ζ37+ζ47−ζ61+ζ71−ζ109+ζ119ζ13−ζ23+ζ37−ζ47+ζ61−ζ71+ζ109−ζ119−ζ7+ζ29−ζ31+ζ53+ζ77−ζ79+ζ101−ζ103ζ7−ζ29+ζ31−ζ53−ζ77+ζ79−ζ101+ζ103000000000000
χ344-404-44-4001-1−3300−2222−22220000001-1−331-1−33ζ13−ζ23+ζ37−ζ47+ζ61−ζ71+ζ109−ζ119−ζ13+ζ23−ζ37+ζ47−ζ61+ζ71−ζ109+ζ119ζ7−ζ29+ζ31−ζ53−ζ77+ζ79−ζ101+ζ103−ζ7+ζ29−ζ31+ζ53+ζ77−ζ79+ζ101−ζ103ζ13−ζ23+ζ37−ζ47+ζ61−ζ71+ζ109−ζ119−ζ13+ζ23−ζ37+ζ47−ζ61+ζ71−ζ109+ζ119ζ7−ζ29+ζ31−ζ53−ζ77+ζ79−ζ101+ζ103−ζ7+ζ29−ζ31+ζ53+ζ77−ζ79+ζ101−ζ103000000000000
χ354-404-44-400-22000022−2222−22000000-2200-2200−222−2−222−2000000000000
χ364-404-44-400-220000−2222−2222000000-2200-22002−2−222−2−22000000000000
χ374-404-4-44001-13−300−2i22i22i2−2i20000001-13−3-11−33−ζ13−ζ23−ζ37−ζ47−ζ61−ζ71−ζ109−ζ119ζ13+ζ23+ζ37+ζ47+ζ61+ζ71+ζ109+ζ119ζ7+ζ29+ζ31+ζ53+ζ77+ζ79+ζ101+ζ103−ζ7−ζ29−ζ31−ζ53−ζ77−ζ79−ζ101−ζ103ζ13+ζ23+ζ37+ζ47+ζ61+ζ71+ζ109+ζ119−ζ13−ζ23−ζ37−ζ47−ζ61−ζ71−ζ109−ζ119−ζ7−ζ29−ζ31−ζ53−ζ77−ζ79−ζ101−ζ103ζ7+ζ29+ζ31+ζ53+ζ77+ζ79+ζ101+ζ103000000000000
χ384-404-4-44001-13−3002i2−2i2−2i22i20000001-13−3-11−33ζ13+ζ23+ζ37+ζ47+ζ61+ζ71+ζ109+ζ119−ζ13−ζ23−ζ37−ζ47−ζ61−ζ71−ζ109−ζ119−ζ7−ζ29−ζ31−ζ53−ζ77−ζ79−ζ101−ζ103ζ7+ζ29+ζ31+ζ53+ζ77+ζ79+ζ101+ζ103−ζ13−ζ23−ζ37−ζ47−ζ61−ζ71−ζ109−ζ119ζ13+ζ23+ζ37+ζ47+ζ61+ζ71+ζ109+ζ119ζ7+ζ29+ζ31+ζ53+ζ77+ζ79+ζ101+ζ103−ζ7−ζ29−ζ31−ζ53−ζ77−ζ79−ζ101−ζ103000000000000
χ394-404-4-44001-1−3300−2i22i22i2−2i20000001-1−33-113−3−ζ7−ζ29−ζ31−ζ53−ζ77−ζ79−ζ101−ζ103ζ7+ζ29+ζ31+ζ53+ζ77+ζ79+ζ101+ζ103ζ13+ζ23+ζ37+ζ47+ζ61+ζ71+ζ109+ζ119−ζ13−ζ23−ζ37−ζ47−ζ61−ζ71−ζ109−ζ119ζ7+ζ29+ζ31+ζ53+ζ77+ζ79+ζ101+ζ103−ζ7−ζ29−ζ31−ζ53−ζ77−ζ79−ζ101−ζ103−ζ13−ζ23−ζ37−ζ47−ζ61−ζ71−ζ109−ζ119ζ13+ζ23+ζ37+ζ47+ζ61+ζ71+ζ109+ζ119000000000000
χ404-404-4-44001-1−33002i2−2i2−2i22i20000001-1−33-113−3ζ7+ζ29+ζ31+ζ53+ζ77+ζ79+ζ101+ζ103−ζ7−ζ29−ζ31−ζ53−ζ77−ζ79−ζ101−ζ103−ζ13−ζ23−ζ37−ζ47−ζ61−ζ71−ζ109−ζ119ζ13+ζ23+ζ37+ζ47+ζ61+ζ71+ζ109+ζ119−ζ7−ζ29−ζ31−ζ53−ζ77−ζ79−ζ101−ζ103ζ7+ζ29+ζ31+ζ53+ζ77+ζ79+ζ101+ζ103ζ13+ζ23+ζ37+ζ47+ζ61+ζ71+ζ109+ζ119−ζ13−ζ23−ζ37−ζ47−ζ61−ζ71−ζ109−ζ119000000000000
χ414-404-4-4400-220000−2i22i22i2−2i2000000-22002-200i2−i2−i2i2−i2i2i2−i2000000000000
χ424-404-4-4400-2200002i2−2i2−2i22i2000000-22002-200−i2i2i2−i2i2−i2−i2i2000000000000
χ4366-666662-20000-6-60000002-22-20000000000000000000000000000
χ4466-666-6-62-20000-660000002-2-220000000000000000000000000000
χ45888-2-20088-4-4-4-4-20000000-2-2001111000000000000000000000000
χ4688-8-2-200-88-4-444200000002-20011-1-1000000000000000000000000
χ47121212-3-300-4-40000-3000004-411000000000000000000-1-11100000000
χ48121212-3-300-4-40000-300000-441100000000000000000011-1-100000000
χ491212-12-3-3004-4000030000000-11000000000000000000−555−500000000
χ501212-12-3-3004-4000030000000-110000000000000000005−5−5500000000
χ5116-160-4400004-443−43000000000000-11−33000000000000000000000000
χ5216-160-4400004-4−4343000000000000-113−3000000000000000000000000
χ5316-160-440000-88000000000000002-200000000000000000000000000

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