Finite Group Databasebeta

← Group #68708

Character table — Group #68708

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51
size112222222222244444444448888888888888888121212121212121224242424
order12222344446121244446661212124488121212121212121224242424444444442488
χ1111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ911-11-1111-1-1111ii−i−i-11-11-1-11-1i−iii−i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i
χ1011-11-1111-1-1111ii−i−i-11-11-1-11-1i−iii−i−i11-1-1ii−i−i-1-111−i−iii-11−ii
χ1111-11-1111-1-1111ii−i−i-11-11-1-1-11−iiii−i−i-1-111−i−iii11-1-1ii−i−i-11−ii
χ1211-11-1111-1-1111ii−i−i-11-11-1-1-11−iiii−i−i-1-111−i−iii-1-111−i−iii1-1i−i
χ1311-11-1111-1-1111−i−iii-11-11-1-11-1−ii−i−iii11-1-1−i−iii11-1-1−i−iii1-1−ii
χ1411-11-1111-1-1111−i−iii-11-11-1-11-1−ii−i−iii11-1-1−i−iii-1-111ii−i−i-11i−i
χ1511-11-1111-1-1111−i−iii-11-11-1-1-11i−i−i−iii-1-111ii−i−i11-1-1−i−iii-11i−i
χ1611-11-1111-1-1111−i−iii-11-11-1-1-11i−i−i−iii-1-111ii−i−i-1-111ii−i−i1-1−ii
χ17222222-2-2-2-22-2-20000222-2-2-200000000000000002-22-200000000
χ18222222-2-2-2-22-2-20000222-2-2-20000000000000000-22-2200000000
χ1922222-12222-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2022222-12222-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111000000000000
χ2122222-12222-1-1-1-2-2-2-2-1-1-1-1-1-122-2-21111-1-1-1-11111000000000000
χ2222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-2-22211111111-1-1-1-1000000000000
χ23222-2-222-22-22222i−2i2i−2i2-2-2-2-2200002i−2i2i−2i00000000000000000000
χ24222-2-222-22-2222−2i2i−2i2i2-2-2-2-220000−2i2i−2i2i00000000000000000000
χ25222-2-22-22-222-2-200002-2-222-2000000000000000000002i−2i2i−2i0000
χ26222-2-22-22-222-2-200002-2-222-200000000000000000000−2i2i−2i2i0000
χ27222-2-2-12-22-2-1-1-12i−2i2i−2i-11111-10000−ii−ii3−33−3−i3i3−i3i3000000000000
χ28222-2-2-12-22-2-1-1-12i−2i2i−2i-11111-10000−ii−ii−33−33i3−i3i3−i3000000000000
χ29222-2-2-12-22-2-1-1-1−2i2i−2i2i-11111-10000i−ii−i3−33−3i3−i3i3−i3000000000000
χ30222-2-2-12-22-2-1-1-1−2i2i−2i2i-11111-10000i−ii−i−33−33−i3i3−i3i3000000000000
χ3122-22-22-2-2222-2-20000-22-2-22200000000000000002-2-2200000000
χ3222-22-22-2-2222-2-20000-22-2-2220000000000000000-222-200000000
χ3322-22-2-122-2-2-1-1-12i2i−2i−2i1-11-1112-22i−2i−i−iii-1-111−i−iii000000000000
χ3422-22-2-122-2-2-1-1-12i2i−2i−2i1-11-111-22−2i2i−i−iii11-1-1ii−i−i000000000000
χ3522-22-2-122-2-2-1-1-1−2i−2i2i2i1-11-1112-2−2i2iii−i−i-1-111ii−i−i000000000000
χ3622-22-2-122-2-2-1-1-1−2i−2i2i2i1-11-111-222i−2iii−i−i11-1-1−i−iii000000000000
χ3722-2-2222-2-222222-2-22-2-22-22-200002-2-2200000000000000000000
χ3822-2-2222-2-22222-222-2-2-22-22-20000-222-200000000000000000000
χ3922-2-222-222-22-2-20000-2-222-22000000000000000000002-2-220000
χ4022-2-222-222-22-2-20000-2-222-2200000000000000000000-222-20000
χ4122-2-22-12-2-22-1-1-12-2-2211-11-110000-111-13−3−33−333−3000000000000
χ4222-2-22-12-2-22-1-1-12-2-2211-11-110000-111-1−333−33−3−33000000000000
χ4322-2-22-12-2-22-1-1-1-222-211-11-1100001-1-113−3−333−3−33000000000000
χ4422-2-22-12-2-22-1-1-1-222-211-11-1100001-1-11−333−3−333−3000000000000
χ4544444-2-4-4-4-4-2220000-2-2-22220000000000000000000000000000
χ46444-4-4-2-44-44-2220000-222-2-220000000000000000000000000000
χ4744-44-4-2-4-444-22200002-222-2-20000000000000000000000000000
χ4844-4-44-2-444-4-222000022-2-22-20000000000000000000000000000
χ498-800080000-80000000000000000000000000000000000000000
χ508-8000-40000443−4300000000000000000000000000000000000000
χ518-8000-400004−434300000000000000000000000000000000000000

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