Finite Group Databasebeta

← Group #72209591

Character table — Group #72209591

Order 2160.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31
size111111727272727272727272727272909090909090909090120120120120
order12336655101015151515303030304881212242424243366
χ11111111111111111111111111111111
χ233−3−3i32−3+3i32−3−3i32−3+3i321+521−521+521−52ζ4+ζ76ζ28+ζ52ζ44+ζ116ζ68+ζ92ζ4+ζ76ζ28+ζ52ζ44+ζ116ζ68+ζ92-1111+i321−i32−1−i32−1−i32−1+i32−1+i320000
χ333−3−3i32−3+3i32−3−3i32−3+3i321−521+521−521+52ζ28+ζ52ζ4+ζ76ζ68+ζ92ζ44+ζ116ζ28+ζ52ζ4+ζ76ζ68+ζ92ζ44+ζ116-1111+i321−i32−1−i32−1−i32−1+i32−1+i320000
χ433−3+3i32−3−3i32−3+3i32−3−3i321+521−521+521−52ζ44+ζ116ζ68+ζ92ζ4+ζ76ζ28+ζ52ζ44+ζ116ζ68+ζ92ζ4+ζ76ζ28+ζ52-1111−i321+i32−1+i32−1+i32−1−i32−1−i320000
χ533−3+3i32−3−3i32−3+3i32−3−3i321−521+521−521+52ζ68+ζ92ζ44+ζ116ζ28+ζ52ζ4+ζ76ζ68+ζ92ζ44+ζ116ζ28+ζ52ζ4+ζ76-1111−i321+i32−1+i32−1+i32−1−i32−1−i320000
χ64-444-4-4-1-111-1-1-1-111110000000001-22-1
χ74-444-4-4-1-111-1-1-1-11111000000000-21-12
χ85555550000000000001-1-111-1-1-1-12-1-12
χ95555550000000000001-1-111-1-1-1-1-122-1
χ1066−3−3i3−3+3i3−3−3i3−3+3i31111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32200−1−i3−1+i300000000
χ1166−3+3i3−3−3i3−3+3i3−3−3i31111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32200−1+i3−1−i300000000
χ126-6−3−3i3−3+3i33+3i33−3i311-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3202−200−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+ζ1090000
χ136-6−3−3i3−3+3i33+3i33−3i311-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i320−2200ζ23−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−ζ1090000
χ146-6−3+3i3−3−3i33−3i33+3i311-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3202−200−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−ζ1190000
χ156-6−3+3i3−3−3i33−3i33+3i311-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i320−2200ζ7−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+ζ1190000
χ168888881+521−521+521−521−521+521−521+521−521+521−521+52000000000-1-1-1-1
χ178888881−521+521−521+521+521−521+521−521+521−521+521−52000000000-1-1-1-1
χ188-888-8-81+521−52−1−52−1+521−521+521−521+52−1+52−1−52−1+52−1−52000000000-1-111
χ198-888-8-81−521+52−1+52−1−521+521−521+521−52−1−52−1+52−1−52−1+52000000000-1-111
χ20999999-1-1-1-1-1-1-1-1-1-1-1-11111111110000
χ2199−9−9i32−9+9i32−9−9i32−9+9i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i320000
χ2299−9+9i32−9−9i32−9+9i32−9−9i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i320000
χ23101010101010000000000000-200-2-200001111
χ2410-101010-10-1000000000000002−2002−2−2211-1-1
χ2510-101010-10-100000000000000−2200−222−211-1-1
χ2612-12−6−6i3−6+6i36+6i36−6i3−1−52−1+521+521−52−ζ4−ζ76−ζ28−ζ52−ζ44−ζ116−ζ68−ζ92ζ4+ζ76ζ28+ζ52ζ44+ζ116ζ68+ζ920000000000000
χ2712-12−6−6i3−6+6i36+6i36−6i3−1+52−1−521−521+52−ζ28−ζ52−ζ4−ζ76−ζ68−ζ92−ζ44−ζ116ζ28+ζ52ζ4+ζ76ζ68+ζ92ζ44+ζ1160000000000000
χ2812-12−6+6i3−6−6i36−6i36+6i3−1−52−1+521+521−52−ζ44−ζ116−ζ68−ζ92−ζ4−ζ76−ζ28−ζ52ζ44+ζ116ζ68+ζ92ζ4+ζ76ζ28+ζ520000000000000
χ2912-12−6+6i3−6−6i36−6i36+6i3−1+52−1−521−521+52−ζ68−ζ92−ζ44−ζ116−ζ28−ζ52−ζ4−ζ76ζ68+ζ92ζ44+ζ116ζ28+ζ52ζ4+ζ760000000000000
χ301515−15−15i32−15+15i32−15−15i32−15+15i32000000000000-1-1-11+i321−i321+i321+i321−i321−i320000
χ311515−15+15i32−15−15i32−15+15i32−15−15i32000000000000-1-1-11−i321+i321−i321−i321+i321+i320000

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