Finite Group Databasebeta

← Group #67484

Character table — Group #67484

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42
size112222222444444444488888888888888888242424244848
order122344612122466688121212888882424242424242424242424241616161644
χ1111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1
χ311111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ5111111111-1-11-1-1-1-11-1-11ii−i−i11-1-1iiii−i−i−i−iii−i−i1-1
χ6111111111-1-11-1-1-1-11-1-11ii−i−i11-1-1iiii−i−i−i−i−i−iii-11
χ7111111111-1-11-1-1-1-11-1-11−i−iii11-1-1−i−i−i−iiiiiii−i−i-11
χ8111111111-1-11-1-1-1-11-1-11−i−iii11-1-1−i−i−i−iiiii−i−iii1-1
χ922222222222222-2-2222-20000-2-2-2-200000000000000
χ10222222222-2-22-2-2222-2-2-20000-2-22200000000000000
χ112222-2-22-2-22-222200-2-2-200000000000000000−i2i2−i2i200
χ122222-2-22-2-22-222200-2-2-200000000000000000i2−i2i2−i200
χ132222-2-22-2-2-222-2-200-222000000000000000002−2−2200
χ142222-2-22-2-2-222-2-200-22200000000000000000−222−200
χ15222-122-1-1-122-1-1-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1000000
χ16222-122-1-1-122-1-1-122-1-1-12-2-2-2-2-1-1-1-111111111000000
χ17222-122-1-1-122-1-1-1-2-2-1-1-1-200001111−i3−i3i3i3−i3−i3i3i3000000
χ18222-122-1-1-122-1-1-1-2-2-1-1-1-200001111i3i3−i3−i3i3i3−i3−i3000000
χ19222-122-1-1-1-2-2-11122-111-2000011-1-133−3−3−3−333000000
χ20222-122-1-1-1-2-2-11122-111-2000011-1-1−3−33333−3−3000000
χ21222-122-1-1-1-2-2-111-2-2-11122i2i−2i−2i-1-111−i−i−i−iiiii000000
χ22222-122-1-1-1-2-2-111-2-2-1112−2i−2i2i2i-1-111iiii−i−i−i−i000000
χ2322-222-222200-2002i−2i-20001+i−1−i1−i−1+i002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000
χ2422-222-222200-2002i−2i-2000−1−i1+i−1+i1−i002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000
χ2522-222-222200-200−2i2i-20001−i−1+i1+i−1−i00−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000
χ2622-222-222200-200−2i2i-2000−1+i1−i−1−i1+i00−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000
χ2722-2-12-2-1-1-1001−i3i32i−2i1−i3i301+i−1−i1−i−1+i3−3−ii−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22000000
χ2822-2-12-2-1-1-1001−i3i32i−2i1−i3i30−1−i1+i−1+i1−i3−3−iiζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22000000
χ2922-2-12-2-1-1-1001−i3i3−2i2i1−i3i301−i−1+i1+i−1−i−33i−i−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22000000
χ3022-2-12-2-1-1-1001−i3i3−2i2i1−i3i30−1+i1−i−1−i1+i−33i−iζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22000000
χ3122-2-12-2-1-1-1001i3−i32i−2i1i3−i301+i−1−i1−i−1+i−33−ii−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14000000
χ3222-2-12-2-1-1-1001i3−i32i−2i1i3−i30−1−i1+i−1+i1−i−33−iiζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14000000
χ3322-2-12-2-1-1-1001i3−i3−2i2i1i3−i301−i−1+i1+i−1−i3−3i−i−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14000000
χ3422-2-12-2-1-1-1001i3−i3−2i2i1i3−i30−1+i1−i−1−i1+i3−3i−iζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14000000
χ35444-2-4-4-2224-4-2-2-20022200000000000000000000000
χ36444-2-4-4-222-44-222002-2-200000000000000000000000
χ3744-44-444-4-400-4000040000000000000000000000000
χ3844-4-2-44-222002−2i32i300-22i3−2i300000000000000000000000
χ3944-4-2-44-2220022i3−2i300-2−2i32i300000000000000000000000
χ408-80800-800000000000000000000000000000000000
χ418-80-400443−43000000000000000000000000000000000
χ428-80-4004−4343000000000000000000000000000000000

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