Finite Group Databasebeta

← Group #150548

Character table — Group #150548

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size11112222444444488888888888888888161616161616161616323232323232
order12222244444444444444444488888888488888888448888
χ111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-111-1-1-1-111111111-1iiii−i−i−i−i-1-1ii−i−i
χ61111111111111111-1-111-1-1-1-111111111-1−i−i−i−iiiii-1-1−i−iii
χ71111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ81111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ9111111-1-11-1-1-1-1-11-11111-1-1-1-11111-1-1-1-11ii−i−iii−i−i1-1i−ii−i
χ10111111-1-11-1-1-1-1-11-11111-1-1-1-11111-1-1-1-11−i−iii−i−iii1-1−ii−ii
χ11111111-1-11-1-1-1-1-11-11111-1-1-1-1-1-1-1-111111ii−i−iii−i−i-11−ii−ii
χ12111111-1-11-1-1-1-1-11-11111-1-1-1-1-1-1-1-111111−i−iii−i−iii-11i−ii−i
χ13111111-1-11-1-1-1-1-11-1-1-11111111111-1-1-1-1-111-1-1-1-111-111-1-11
χ14111111-1-11-1-1-1-1-11-1-1-11111111111-1-1-1-1-1-1-11111-1-1-11-111-1
χ15111111-1-11-1-1-1-1-11-1-1-1111111-1-1-1-11111-111-1-1-1-1111-1-111-1
χ16111111-1-11-1-1-1-1-11-1-1-1111111-1-1-1-11111-1-1-11111-1-11-11-1-11
χ172222222222-2-2-2-22222-2-222-2-200000000-200000000000000
χ182222222222-2-2-2-222-2-2-2-2-2-22200000000200000000000000
χ19222222-2-22-222222-222-2-2-2-22200000000-200000000000000
χ20222222-2-22-222222-2-2-2-2-222-2-200000000200000000000000
χ2122-2-22-200-2022-2-2202i−2i00002i−2i0000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000
χ2222-2-22-200-2022-2-2202i−2i00002i−2i000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000
χ2322-2-22-200-2022-2-220−2i2i0000−2i2i0000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000
χ2422-2-22-200-2022-2-220−2i2i0000−2i2i000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000
χ2522-2-22-200-20-2-222202i−2i0000−2i2i0000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i000000
χ2622-2-22-200-20-2-222202i−2i0000−2i2i000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000
χ2722-2-22-200-20-2-22220−2i2i00002i−2i0000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i000000
χ2822-2-22-200-20-2-22220−2i2i00002i−2i000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000
χ2944444444-440000-4-40000000000000000000000000000000
χ30444444-4-4-4-40000-440000000000000000000000000000000
χ314444-4-4440-40000000000000022-2-222-2-2000000000000000
χ324444-4-4440-400000000000000-2-222-2-222000000000000000
χ334444-4-4-4-4040000000000000022-2-2-2-222000000000000000
χ344444-4-4-4-40400000000000000-2-22222-2-2000000000000000
χ3544-4-44-400400000-4000004-40000000000000000000000000
χ3644-4-44-400400000-400000-440000000000000000000000000
χ374-4-44004-4002-22-200002-20000002i2−2i2002i2−2i2000000000000000
χ384-4-44004-4002-22-200002-2000000−2i22i200−2i22i2000000000000000
χ394-4-44004-400-22-220000-2200002i2−2i2002i2−2i200000000000000000
χ404-4-44004-400-22-220000-220000−2i22i200−2i22i200000000000000000
χ414-4-4400-44002-22-20000-2200002i2−2i200−2i22i200000000000000000
χ424-4-4400-44002-22-20000-220000−2i22i2002i2−2i200000000000000000
χ434-4-4400-4400-22-2200002-20000002i2−2i200−2i22i2000000000000000
χ444-4-4400-4400-22-2200002-2000000−2i22i2002i2−2i2000000000000000
χ4588-8-8-8800000000000000000000000000000000000000000
χ468-88-80000004-4-44000000000000000000000000000000000
χ478-88-8000000-444-4000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).