Finite Group Databasebeta

← Group #10713271

Character table — Group #10713271

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112222222222222444444444444488888888888888161616161616161616161616242424242424242448484848
order12222344446881212666888121212242424241616161624244848484848484848888824242424242424244488161616164488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ9111-1-11-111-1111111-1-1-11-1-1-11111111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1i−ii−iii−i−ii−ii−i
χ10111-1-11-111-1111111-1-1-11-1-1-11111111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1−ii−ii−i−iii−ii−ii
χ11111-1-11-111-1111111-1-1-11-1-1-11111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111i−ii−iii−i−i−ii−ii
χ12111-1-11-111-1111111-1-1-11-1-1-11111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111−ii−ii−i−iiii−ii−i
χ13111-1-11-111-1111111-1-1-11-1-1-111111-1-111-1-1-1-1-1-111111-1-1111-1-1-1-111i−ii−i−i−iiii−i−ii
χ14111-1-11-111-1111111-1-1-11-1-1-111111-1-111-1-1-1-1-1-111111-1-1111-1-1-1-111−ii−iiii−i−i−iii−i
χ15111-1-11-111-1111111-1-1-11-1-1-111111-1-111-1-1-1-1-1-11111-111-1-1-11111-1-1i−ii−i−i−iii−iii−i
χ16111-1-11-111-1111111-1-1-11-1-1-111111-1-111-1-1-1-1-1-11111-111-1-1-11111-1-1−ii−iiii−i−ii−i−ii
χ1722222222222-2-222222-2-2-2222-2-2-2-20000-2-20000000000000000000022-2-200000000
χ1822222222222-2-222222-2-2-2222-2-2-2-20000-2-200000000000000000000-2-22200000000
χ1922222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ2022222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ2122222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-11111000000000000
χ2222222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-1000000000000
χ23222-2-22-222-22-2-2222-2-22-22-2-22-2-2-2-2000022000000000000000000002i−2i−2i2i00000000
χ24222-2-22-222-22-2-2222-2-22-22-2-22-2-2-2-200002200000000000000000000−2i2i2i−2i00000000
χ25222-2-2-1-222-2-122-1-1-111-22-211-1-1-1-1-122-2-211-1-1-1-111112-22-2-1-111-1-111000000000000
χ26222-2-2-1-222-2-122-1-1-111-22-211-1-1-1-1-122-2-211-1-1-1-11111-22-2211-1-111-1-1000000000000
χ27222-2-2-1-222-2-122-1-1-111-22-211-1-1-1-1-1-2-222111111-1-1-1-12-2-22-1-11111-1-1000000000000
χ28222-2-2-1-222-2-122-1-1-111-22-211-1-1-1-1-1-2-222111111-1-1-1-1-222-211-1-1-1-111000000000000
χ2922-22-2222-2-2222-2-2-22-2-2-222-2222-2-200002-20000000000000000000000002-22-20000
χ3022-22-2222-2-2222-2-2-22-2-2-222-2222-2-200002-2000000000000000000000000-22-220000
χ3122-22-2222-2-22-2-2-2-2-22-222-22-22-2-2222-22-2-2222-2-222-2-2000000000000000000000000
χ3222-22-2222-2-22-2-2-2-2-22-222-22-22-2-222-22-22-22-2-222-2-222000000000000000000000000
χ3322-22-2-122-2-2-1-2-2111-1122-2-11-111-1-12-22-21-1-1-111-1-11100003−33−33−33−3000000000000
χ3422-22-2-122-2-2-1-2-2111-1122-2-11-111-1-12-22-21-1-1-111-1-1110000−33−33−33−33000000000000
χ3522-22-2-122-2-2-1-2-2111-1122-2-11-111-1-1-22-221-111-1-111-1-100003−33−3−33−33000000000000
χ3622-22-2-122-2-2-1-2-2111-1122-2-11-111-1-1-22-221-111-1-111-1-10000−33−333−33−3000000000000
χ3722-2-222-22-22222-2-2-2-222-2-2-22222-2-20000-220000000000000000000000002i−2i−2i2i0000
χ3822-2-222-22-22222-2-2-2-222-2-2-22222-2-20000-22000000000000000000000000−2i2i2i−2i0000
χ3922-2-222-22-222-2-2-2-2-2-22-222-222-2-2222-2-222-222-2-2-2-222000000000000000000000000
χ4022-2-222-22-222-2-2-2-2-2-22-222-222-2-222-222-22-2-2-22222-2-2000000000000000000000000
χ4122-2-22-1-22-22-1-2-21111-1-2221-1-111-1-12-2-22-11-1-11111-1-100003−3−333−3−33000000000000
χ4222-2-22-1-22-22-1-2-21111-1-2221-1-111-1-12-2-22-11-1-11111-1-10000−333−3−333−3000000000000
χ4322-2-22-1-22-22-1-2-21111-1-2221-1-111-1-1-222-2-1111-1-1-1-11100003−3−33−333−3000000000000
χ4422-2-22-1-22-22-1-2-21111-1-2221-1-111-1-1-222-2-1111-1-1-1-1110000−333−33−3−33000000000000
χ45444444-4-4-4-4400-4-4444000-4-4-4000000000000000000000000000000000000000000
χ4644444-24444-2-4-4-2-2-2-2-2-4-4-4-2-2-2222200002200000000000000000000000000000000
χ4744444-2-4-4-4-4-20022-2-2-20002220000000000i6−i6i6−i6i6−i6i6−i6000000000000000000000000
χ4844444-2-4-4-4-4-20022-2-2-20002220000000000−i6i6−i6i6−i6i6−i6i6000000000000000000000000
χ49444-4-444-4-44400-4-44-4-400044-4000000000000000000000000000000000000000000
χ50444-4-4-24-4-44-20022-222000-2-220000000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ51444-4-4-24-4-44-20022-222000-2-220000000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ52444-4-4-2-444-4-2-4-4-2-2-2224-4422-222220000-2-200000000000000000000000000000000
χ5344-44-44-4-44440044-44-4000-44-4000000000000000000000000000000000000000000
χ5444-44-4-244-4-4-244222-22-4-44-22-2-2-2220000-2200000000000000000000000000000000
χ5544-44-4-2-4-444-200-2-22-220002-220000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ5644-44-4-2-4-444-200-2-22-220002-220000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ5744-4-4444-44-440044-4-440004-4-4000000000000000000000000000000000000000000
χ5844-4-44-24-44-4-200-2-222-2000-2220000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ5944-4-44-24-44-4-200-2-222-2000-2220000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ6044-4-44-2-44-44-2442222-24-4-42-2-2-2-22200002-200000000000000000000000000000000
χ618-800080000-8−4i24i200000000000−4i24i20000000000000000000000000000000000000000
χ628-800080000-84i2−4i2000000000004i2−4i20000000000000000000000000000000000000000
χ638-8000-400004−4i24i243−430000000002i2−2i22i6−2i600000000000000000000000000000000000000
χ648-8000-400004−4i24i2−43430000000002i2−2i2−2i62i600000000000000000000000000000000000000
χ658-8000-4000044i2−4i243−43000000000−2i22i2−2i62i600000000000000000000000000000000000000
χ668-8000-4000044i2−4i2−4343000000000−2i22i22i6−2i600000000000000000000000000000000000000

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