Finite Group Databasebeta

← Group #67489

Character table — Group #67489

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45
size11112222224444444444888888888888888882424242424242424
order122222366622446666664444412121212121212121212121222448888
χ1111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-1-1-111-1-1-1-11ii−i−i11-1-1iiii−i−i−i−i11-1-1ii−i−i
χ61111111111-1-1-1-111-1-1-1-11ii−i−i11-1-1iiii−i−i−i−i-1-111−i−iii
χ71111111111-1-1-1-111-1-1-1-11−i−iii11-1-1−i−i−i−iiiii11-1-1−i−iii
χ81111111111-1-1-1-111-1-1-1-11−i−iii11-1-1−i−i−i−iiiii-1-111ii−i−i
χ9222222222222-2-2222222-20000-2-2-2-20000000000000000
χ102222222222-2-22222-2-2-2-2-20000-2-2220000000000000000
χ11222222-1-1-1-12222-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-100000000
χ12222222-1-1-1-12222-1-1-1-1-1-12-2-2-2-2-1-1-1-11111111100000000
χ13222222-1-1-1-122-2-2-1-1-1-1-1-1-200001111−i3−i3i3i3−i3−i3i3i300000000
χ14222222-1-1-1-122-2-2-1-1-1-1-1-1-200001111i3i3−i3−i3i3i3−i3−i300000000
χ15222222-1-1-1-1-2-222-1-11111-2000011-1-133−3−3−3−33300000000
χ16222222-1-1-1-1-2-222-1-11111-2000011-1-1−3−33333−3−300000000
χ17222222-1-1-1-1-2-2-2-2-1-1111122i2i−2i−2i-1-111−i−i−i−iiiii00000000
χ18222222-1-1-1-1-2-2-2-2-1-111112−2i−2i2i2i-1-111iiii−i−i−i−i00000000
χ1922-2-22-222-2-2002i−2i2-2000001+i−1−i1−i−1+i002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ2022-2-22-222-2-2002i−2i2-200000−1−i1+i−1+i1−i002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ2122-2-22-222-2-200−2i2i2-2000001−i−1+i1+i−1−i00−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ2222-2-22-222-2-200−2i2i2-200000−1+i1−i−1−i1+i00−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ2322-2-22-2-1-111002i−2i-11−i3i3−i3i301+i−1−i1−i−1+i3−3−ii−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ2200000000
χ2422-2-22-2-1-111002i−2i-11−i3i3−i3i30−1−i1+i−1+i1−i3−3−iiζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ2200000000
χ2522-2-22-2-1-111002i−2i-11i3−i3i3−i301+i−1−i1−i−1+i−33−ii−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ1400000000
χ2622-2-22-2-1-111002i−2i-11i3−i3i3−i30−1−i1+i−1+i1−i−33−iiζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ1400000000
χ2722-2-22-2-1-11100−2i2i-11−i3i3−i3i301−i−1+i1+i−1−i−33i−i−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ2200000000
χ2822-2-22-2-1-11100−2i2i-11−i3i3−i3i30−1+i1−i−1−i1+i−33i−iζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ2200000000
χ2922-2-22-2-1-11100−2i2i-11i3−i3i3−i301−i−1+i1+i−1−i3−3i−i−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ1400000000
χ3022-2-22-2-1-11100−2i2i-11i3−i3i3−i30−1+i1−i−1−i1+i3−3i−iζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ1400000000
χ3122-2-2-2222-2-22-200-2222-2-2000000000000000000000−i2i2−i2i2
χ3222-2-2-2222-2-22-200-2222-2-2000000000000000000000i2−i2i2−i2
χ3322-2-2-2222-2-2-2200-22-2-2220000000000000000000002−2−22
χ3422-2-2-2222-2-2-2200-22-2-222000000000000000000000−222−2
χ354444-4-444440000-4-400000000000000000000000000000
χ364444-4-4-2-2-2-2000022−2i32i32i3−2i30000000000000000000000000
χ374444-4-4-2-2-2-20000222i3−2i3−2i32i30000000000000000000000000
χ3844-4-4-44-2-2224-4002-2-2-2220000000000000000000000000
χ3944-4-4-44-2-222-44002-222-2-20000000000000000000000000
χ404-44-4004-44-4000000000000000000000000000002-20000
χ414-44-4004-44-400000000000000000000000000000-220000
χ424-4-44004-4-440000000000000000000000000002-2000000
χ434-4-44004-4-44000000000000000000000000000-22000000
χ448-88-800-44-4400000000000000000000000000000000000
χ458-8-8800-444-400000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.