Finite Group Databasebeta

← Group #10877378

Character table — Group #10877378

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222224444444444444444444444444488888888888888888888888888888888242424242424242448484848
order12442223444612122244666666688881212121212121224242424888888888824242424242424242424242424242424242424242424244488884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ911111111111111-1-1-1-1111-1-1-1-1111111-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1111-11-1
χ1011111111111111-1-1-1-1111-1-1-1-1111111-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-11-11
χ1111111111111111-1-1-1-1111-1-1-1-1111111-1-1-1-111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-111-11-11
χ1211111111111111-1-1-1-1111-1-1-1-1111111-1-1-1-111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-11-11-1
χ1311111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-11-1-11
χ1411111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-111-1
χ1511111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1111111-1-111-1-1-111-1
χ1611111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1111-1-11
χ172222222-1222-1-1-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ182222222-1222-1-1-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2221111111111111111-1-1-1-1-1-1000000000000
χ192222222-1222-1-1-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-111112222-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111000000000000
χ202222222-1222-1-1-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-11111-2-2-2-22222-2-211111111-1-1-1-1-1-1-1-1111111000000000000
χ212222222-1222-1-1-1-2-2-2-2-1-1-111112222-1-11111-1-1-1-1-122-2-222-2-2-2-2-1-1-1-11111-1-1-1-11111-1-11111000000000000
χ222222222-1222-1-1-1-2-2-2-2-1-1-111112222-1-11111-1-1-1-1-1-2-222-2-222-2-21111-1-1-1-11111-1-1-1-1-1-11111000000000000
χ232222222-1222-1-1-1-2-2-2-2-1-1-11111-2-2-2-2-1-11111-1111122-2-2-2-22222-1-1-1-111111111-1-1-1-111-1-1-1-1000000000000
χ242222222-1222-1-1-1-2-2-2-2-1-1-11111-2-2-2-2-1-11111-11111-2-22222-2-2221111-1-1-1-1-1-1-1-1111111-1-1-1-1000000000000
χ2522222-2-22-2-222222-22-22-2-222-2-222-2-2-2-222-2-222222000000002-20000000000000000-2-222-2-2000000000000
χ2622222-2-22-2-222222-22-22-2-222-2-2-2-222-2-222-2-22-2-2-2-200000000-22000000000000000022-2-222000000000000
χ2722222-2-22-2-22222-22-222-2-2-2-22222-2-2-2-2-2-2222222200000000-220000000000000000-2-2-2-222000000000000
χ2822222-2-22-2-22222-22-222-2-2-2-222-2-222-2-2-2-2222-2-2-2-2000000002-200000000000000002222-2-2000000000000
χ2922222-2-2-1-2-22-1-1-12-22-2-111-1-11122-2-211-1-111-1-1-1-1-1000000002-2−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i311-1-111000000000000
χ3022222-2-2-1-2-22-1-1-12-22-2-111-1-11122-2-211-1-111-1-1-1-1-1000000002-2i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i311-1-111000000000000
χ3122222-2-2-1-2-22-1-1-12-22-2-111-1-111-2-22211-1-111-1111100000000-22−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3-1-111-1-1000000000000
χ3222222-2-2-1-2-22-1-1-12-22-2-111-1-111-2-22211-1-111-1111100000000-22i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3-1-111-1-1000000000000
χ3322222-2-2-1-2-22-1-1-1-22-22-11111-1-122-2-21111-1-1-1-1-1-1-100000000-22−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i31111-1-1000000000000
χ3422222-2-2-1-2-22-1-1-1-22-22-11111-1-122-2-21111-1-1-1-1-1-1-100000000-22i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i31111-1-1000000000000
χ3522222-2-2-1-2-22-1-1-1-22-22-11111-1-1-2-2221111-1-1-11111000000002-2−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3-1-1-1-111000000000000
χ3622222-2-2-1-2-22-1-1-1-22-22-11111-1-1-2-2221111-1-1-11111000000002-2i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3-1-1-1-111000000000000
χ3722-2-22222-2-2-22-2-22-2-2222222-2-20000-2-2-2-222-200000000000000000000000000000000000000002i−2i2i−2i0000
χ3822-2-22222-2-2-22-2-22-2-2222222-2-20000-2-2-2-222-20000000000000000000000000000000000000000−2i2i−2i2i0000
χ3922-2-22222-2-2-22-2-2-222-2222-2-2220000-2-222-2-2-200000000000000000000000000000000000000002i−2i−2i2i0000
χ4022-2-22222-2-2-22-2-2-222-2222-2-2220000-2-222-2-2-20000000000000000000000000000000000000000−2i2i2i−2i0000
χ4122-2-22-2-2222-22-2-222-2-22-2-22222000022-2-2-2-2-20000000000000000000000000000000000002-22-200000000
χ4222-2-22-2-2222-22-2-222-2-22-2-22222000022-2-2-2-2-2000000000000000000000000000000000000-22-2200000000
χ4322-2-22-2-2222-22-2-2-2-2222-2-2-2-2-2-20000222222-20000000000000000000000000000000000002-2-2200000000
χ4422-2-22-2-2222-22-2-2-2-2222-2-2-2-2-2-20000222222-2000000000000000000000000000000000000-222-200000000
χ4522-2-2-22-222-222-2-20000-22-200002-22-22-20000222-2-2002i−2i002i−2i0000002i−2i2i−2i00002i−2i2i−2i2-20000000000000000
χ4622-2-2-22-222-222-2-20000-22-200002-22-22-20000222-2-200−2i2i00−2i2i000000−2i2i−2i2i0000−2i2i−2i2i2-20000000000000000
χ4722-2-2-22-222-222-2-20000-22-20000-22-222-200002-2-222002i−2i00−2i2i0000002i−2i2i−2i0000−2i2i−2i2i-220000000000000000
χ4822-2-2-22-222-222-2-20000-22-20000-22-222-200002-2-22200−2i2i002i−2i000000−2i2i−2i2i00002i−2i2i−2i-220000000000000000
χ4922-2-2-22-2-12-22-11100001-11−i3i3−i3i32-22-2-11−i3i3−i3i3-1-1-111002i−2i002i−2i003−33−3−ii−ii3−33−3−ii−ii-11−i3i3−i3i3000000000000
χ5022-2-2-22-2-12-22-11100001-11−i3i3−i3i32-22-2-11−i3i3−i3i3-1-1-11100−2i2i00−2i2i00−33−33i−ii−i−33−33i−ii−i-11−i3i3−i3i3000000000000
χ5122-2-2-22-2-12-22-11100001-11−i3i3−i3i3-22-22-11−i3i3−i3i3-111-1-1002i−2i00−2i2i003−33−3−ii−ii−33−33i−ii−i1-1i3−i3i3−i3000000000000
χ5222-2-2-22-2-12-22-11100001-11−i3i3−i3i3-22-22-11−i3i3−i3i3-111-1-100−2i2i002i−2i00−33−33i−ii−i3−33−3−ii−ii1-1i3−i3i3−i3000000000000
χ5322-2-2-22-2-12-22-11100001-11i3−i3i3−i32-22-2-11i3−i3i3−i3-1-1-111002i−2i002i−2i00−33−33−ii−ii−33−33−ii−ii-11i3−i3i3−i3000000000000
χ5422-2-2-22-2-12-22-11100001-11i3−i3i3−i32-22-2-11i3−i3i3−i3-1-1-11100−2i2i00−2i2i003−33−3i−ii−i3−33−3i−ii−i-11i3−i3i3−i3000000000000
χ5522-2-2-22-2-12-22-11100001-11i3−i3i3−i3-22-22-11i3−i3i3−i3-111-1-1002i−2i00−2i2i00−33−33−ii−ii3−33−3i−ii−i1-1−i3i3−i3i3000000000000
χ5622-2-2-22-2-12-22-11100001-11i3−i3i3−i3-22-22-11i3−i3i3−i3-111-1-100−2i2i002i−2i003−33−3i−ii−i−33−33−ii−ii1-1−i3i3−i3i3000000000000
χ5722-2-2-2-222-2222-2-20000-2-2200002-2-22-220000222-2-22i−2i002i−2i00002i−2i−2i2i00002i−2i−2i2i0000-220000000000000000
χ5822-2-2-2-222-2222-2-20000-2-2200002-2-22-220000222-2-2−2i2i00−2i2i0000−2i2i2i−2i0000−2i2i2i−2i0000-220000000000000000
χ5922-2-2-2-222-2222-2-20000-2-220000-222-2-2200002-2-2222i−2i00−2i2i00002i−2i−2i2i0000−2i2i2i−2i00002-20000000000000000
χ6022-2-2-2-222-2222-2-20000-2-220000-222-2-2200002-2-222−2i2i002i−2i0000−2i2i2i−2i00002i−2i−2i2i00002-20000000000000000
χ6122-2-2-2-22-1-222-111000011-1−i3i3i3−i32-2-221-1−i3i3i3−i3-1-1-1112i−2i002i−2i0000−iii−i3−3−33−iii−i3−3−331-1−i3i3i3−i3000000000000
χ6222-2-2-2-22-1-222-111000011-1−i3i3i3−i32-2-221-1−i3i3i3−i3-1-1-111−2i2i00−2i2i0000i−i−ii−333−3i−i−ii−333−31-1−i3i3i3−i3000000000000
χ6322-2-2-2-22-1-222-111000011-1−i3i3i3−i3-222-21-1−i3i3i3−i3-111-1-12i−2i00−2i2i0000−iii−i3−3−33i−i−ii−333−3-11i3−i3−i3i3000000000000
χ6422-2-2-2-22-1-222-111000011-1−i3i3i3−i3-222-21-1−i3i3i3−i3-111-1-1−2i2i002i−2i0000i−i−ii−333−3−iii−i3−3−33-11i3−i3−i3i3000000000000
χ6522-2-2-2-22-1-222-111000011-1i3−i3−i3i32-2-221-1i3−i3−i3i3-1-1-1112i−2i002i−2i0000−iii−i−333−3−iii−i−333−31-1i3−i3−i3i3000000000000
χ6622-2-2-2-22-1-222-111000011-1i3−i3−i3i32-2-221-1i3−i3−i3i3-1-1-111−2i2i00−2i2i0000i−i−ii3−3−33i−i−ii3−3−331-1i3−i3−i3i3000000000000
χ6722-2-2-2-22-1-222-111000011-1i3−i3−i3i3-222-21-1i3−i3−i3i3-111-1-12i−2i00−2i2i0000−iii−i−333−3i−i−ii3−3−33-11−i3i3i3−i3000000000000
χ6822-2-2-2-22-1-222-111000011-1i3−i3−i3i3-222-21-1i3−i3−i3i3-111-1-1−2i2i002i−2i0000i−i−ii3−3−33−iii−i−333−3-11−i3i3i3−i3000000000000
χ694444-44-44-44-44440000-44-400000000-440000-4000000000000000000000000000000000000000000000000
χ704444-44-4-2-44-4-2-2-200002-22−2i32i32i3−2i300002-22i3−2i3−2i32i32000000000000000000000000000000000000000000000000
χ714444-44-4-2-44-4-2-2-200002-222i3−2i3−2i32i300002-2−2i32i32i3−2i32000000000000000000000000000000000000000000000000
χ724444-4-4444-4-44440000-4-44000000004-40000-4000000000000000000000000000000000000000000000000
χ734444-4-44-24-4-4-2-2-2000022-2−2i32i3−2i32i30000-222i3−2i32i3−2i32000000000000000000000000000000000000000000000000
χ744444-4-44-24-4-4-2-2-2000022-22i3−2i32i3−2i30000-22−2i32i3−2i32i32000000000000000000000000000000000000000000000000
χ7544-4-4444-2-4-4-4-2224-4-44-2-2-2-2-22200002222-2-22000000000000000000000000000000000000000000000000
χ7644-4-4444-2-4-4-4-222-444-4-2-2-222-2-2000022-2-2222000000000000000000000000000000000000000000000000
χ7744-4-44-4-4-244-4-22244-4-4-222-2-2-2-20000-2-222222000000000000000000000000000000000000000000000000
χ7844-4-44-4-4-244-4-222-4-444-22222220000-2-2-2-2-2-22000000000000000000000000000000000000000000000000
χ798-88i−8i0008000-88i−8i0000000000000000000000000000000000000000000000000000000000000000000000
χ808-88i−8i000-40004−4i4i00000000000000000000002i6−2i626−2600000000000000000000000000000000000000000000
χ818-88i−8i000-40004−4i4i0000000000000000000000−2i62i6−262600000000000000000000000000000000000000000000
χ828-8−8i8i0008000-8−8i8i0000000000000000000000000000000000000000000000000000000000000000000000
χ838-8−8i8i000-400044i−4i00000000000000000000002i6−2i6−262600000000000000000000000000000000000000000000
χ848-8−8i8i000-400044i−4i0000000000000000000000−2i62i626−2600000000000000000000000000000000000000000000

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