Finite Group Databasebeta

← Group #150413

Character table — Group #150413

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222224444444444888888888888888888888161616161616323232323232
order124424444422244444444444444444444444488882488884816161616
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111
χ511111111111-1-1-1-1-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i11-1-111111-1-1-1ii−i−i
χ611111111111-1-1-1-1-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-1-1-11-111−i−iii
χ711111111111-1-1-1-1-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii11-1-111111-1-1-1−i−iii
χ811111111111-1-1-1-1-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-1-1-11-111ii−i−i
χ911111-1-1-1-1111111-1-1-1-11-11111-1-1-1-11111-1-1-1-1-1-11111-1-11-11-11-11-1
χ1011111-1-1-1-1111111-1-1-1-11-11111-1-1-1-11111-1-1-1-1-1-111-1-1111-1-11-11-11
χ1111111-1-1-1-1111111-1-1-1-11-1-1-1-1-11111-1-1-1-11111-1-11111-1-11-11-1-11-11
χ1211111-1-1-1-1111111-1-1-1-11-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-1-111-11-1
χ1311111-1-1-1-111-1-1-1-111111-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111-1-111-11i−i−ii
χ1411111-1-1-1-111-1-1-1-111111-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1-1-111111-1−iii−i
χ1511111-1-1-1-111-1-1-1-111111-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111-1-111-11−iii−i
χ1611111-1-1-1-111-1-1-1-111111-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1-1-111111-1i−i−ii
χ172222222222222222222220000000000000000-2-2-2-20000-2-2000000
χ1822222222222-2-2-2-2-2-2-2-2220000000000000000-2-2220000-22000000
χ1922222-2-2-2-2222222-2-2-2-22-2000000000000000022-2-20000-22000000
χ2022222-2-2-2-222-2-2-2-222222-2000000000000000022220000-2-2000000
χ2122-2-220000-2-2000022-2-2201+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i2i−2i2i−2i000000000000
χ2222-2-220000-2-2000022-2-2201−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−2i2i−2i2i000000000000
χ2322-2-220000-2-2000022-2-220−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2i2i−2i2i000000000000
χ2422-2-220000-2-2000022-2-220−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i2i−2i2i−2i000000000000
χ2522-2-220000-2-20000-2-222201+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−2i2i2i−2i000000000000
χ2622-2-220000-2-20000-2-222201−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i2i−2i−2i2i000000000000
χ2722-2-220000-2-20000-2-22220−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i2i−2i−2i2i000000000000
χ2822-2-220000-2-20000-2-22220−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−2i2i2i−2i000000000000
χ294444444444-400000000-4-400000000000000000000000000000000
χ3044444-4-4-4-44-400000000-4400000000000000000000000000000000
χ3144-4-440000-4444-4-40000-4000000000000000000000000000000000
χ3244-4-440000-44-4-4440000-4000000000000000000000000000000000
χ3344-4-4-44i4i−4i−4i400000000000000000000000000000002-22i−2i00000000
χ3444-4-4-44i4i−4i−4i40000000000000000000000000000000-22−2i2i00000000
χ3544-4-4-4−4i−4i4i4i400000000000000000000000000000002-2−2i2i00000000
χ3644-4-4-4−4i−4i4i4i40000000000000000000000000000000-222i−2i00000000
χ374-44i−4i02+2i−2−2i2−2i−2+2i002-22i−2i2-22i−2i001+i−1−i1−i−1+i1−i−1+i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000000000
χ384-44i−4i02+2i−2−2i2−2i−2+2i002-22i−2i2-22i−2i00−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000000000
χ394-44i−4i02+2i−2−2i2−2i−2+2i00-22−2i2i-22−2i2i001−i−1+i−1−i1+i−1−i1+i1−i−1+i1+i−1−i−1+i1−i−1+i1−i1+i−1−i0000000000000000
χ404-44i−4i02+2i−2−2i2−2i−2+2i00-22−2i2i-22−2i2i00−1+i1−i1+i−1−i1+i−1−i−1+i1−i−1−i1+i1−i−1+i1−i−1+i−1−i1+i0000000000000000
χ414-44i−4i0−2−2i2+2i−2+2i2−2i002-22i−2i-22−2i2i001+i−1−i1−i−1+i−1+i1−i−1−i1+i1−i−1+i1+i−1−i−1−i1+i−1+i1−i0000000000000000
χ424-44i−4i0−2−2i2+2i−2+2i2−2i002-22i−2i-22−2i2i00−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1+i1−i−1−i1+i1+i−1−i1−i−1+i0000000000000000
χ434-44i−4i0−2−2i2+2i−2+2i2−2i00-22−2i2i2-22i−2i001−i−1+i−1−i1+i1+i−1−i−1+i1−i1+i−1−i−1+i1−i1−i−1+i−1−i1+i0000000000000000
χ444-44i−4i0−2−2i2+2i−2+2i2−2i00-22−2i2i2-22i−2i00−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000000000000000
χ454-4−4i4i02−2i−2+2i2+2i−2−2i002-2−2i2i2-2−2i2i001−i−1+i1+i−1−i1+i−1−i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000000000000
χ464-4−4i4i02−2i−2+2i2+2i−2−2i002-2−2i2i2-2−2i2i00−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000000000000
χ474-4−4i4i02−2i−2+2i2+2i−2−2i00-222i−2i-222i−2i001+i−1−i−1+i1−i−1+i1−i1+i−1−i1−i−1+i−1−i1+i−1−i1+i1−i−1+i0000000000000000
χ484-4−4i4i02−2i−2+2i2+2i−2−2i00-222i−2i-222i−2i00−1−i1+i1−i−1+i1−i−1+i−1−i1+i−1+i1−i1+i−1−i1+i−1−i−1+i1−i0000000000000000
χ494-4−4i4i0−2+2i2−2i−2−2i2+2i002-2−2i2i-222i−2i001−i−1+i1+i−1−i−1−i1+i−1+i1−i1+i−1−i1−i−1+i−1+i1−i−1−i1+i0000000000000000
χ504-4−4i4i0−2+2i2−2i−2−2i2+2i002-2−2i2i-222i−2i00−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1−i1+i−1+i1−i1−i−1+i1+i−1−i0000000000000000
χ514-4−4i4i0−2+2i2−2i−2−2i2+2i00-222i−2i2-2−2i2i001+i−1−i−1+i1−i1−i−1+i−1−i1+i1−i−1+i−1−i1+i1+i−1−i−1+i1−i0000000000000000
χ524-4−4i4i0−2+2i2−2i−2−2i2+2i00-222i−2i2-2−2i2i00−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000000000000000
χ538888-80000-80000000000000000000000000000000000000000000

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