Finite Group Databasebeta

← Group #70531

Character table — Group #70531

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size11112222222222222244444444444444448888888888882424242424242424
order1244222344466612121212444466121212121212121212128888242424242424242422448888
χ1111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111
χ5111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-11-1-1-111
χ8111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-1111-1-1
χ92222222-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000
χ102222222-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000
χ112222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-1111100000000
χ122222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2221111-1-1-1-100000000
χ1322222-2-22-22-22-2-222-2-200002-22-2000000000000000000000000002i−2i
χ1422222-2-22-22-22-2-222-2-200002-22-200000000000000000000000000−2i2i
χ152222-22-22-2-222-2-222-2-20000-22-220000000000000000000000002i−2i00
χ162222-22-22-2-222-2-222-2-20000-22-22000000000000000000000000−2i2i00
χ172222-2-2222-2-222222220000-2-2-2-2000000002-20022-2-2000000000000
χ182222-2-2222-2-222222220000-2-2-2-200000000-2200-2-222000000000000
χ192222-2-22-12-2-2-1-1-1-1-1-1-100001111−i3−i3−i3−i3i3i3i3i32-200-1-111−i3−i3i3i300000000
χ202222-2-22-12-2-2-1-1-1-1-1-1-100001111−i3−i3−i3−i3i3i3i3i3-220011-1-1i3i3−i3−i300000000
χ212222-2-22-12-2-2-1-1-1-1-1-1-100001111i3i3i3i3−i3−i3−i3−i32-200-1-111i3i3−i3−i300000000
χ222222-2-22-12-2-2-1-1-1-1-1-1-100001111i3i3i3i3−i3−i3−i3−i3-220011-1-1−i3−i3i3i300000000
χ2322-2-22222-2-2-2222-2-2-2-2000022-2-200000000002i−2i00002i−2i2i−2i00000000
χ2422-2-22222-2-2-2222-2-2-2-2000022-2-20000000000−2i2i0000−2i2i−2i2i00000000
χ2522-2-2222-1-2-2-2-1-1-111110000-1-111−i3−i3i3i3−i3−i3i3i3002i−2i3−33−3−ii−ii00000000
χ2622-2-2222-1-2-2-2-1-1-111110000-1-111−i3−i3i3i3−i3−i3i3i300−2i2i−33−33i−ii−i00000000
χ2722-2-2222-1-2-2-2-1-1-111110000-1-111i3i3−i3−i3i3i3−i3−i3002i−2i−33−33−ii−ii00000000
χ2822-2-2222-1-2-2-2-1-1-111110000-1-111i3i3−i3−i3i3i3−i3−i300−2i2i3−33−3i−ii−i00000000
χ2922-2-22-2-222-222-2-2-2-22200002-2-220000000000000000000020-200000
χ3022-2-22-2-222-222-2-2-2-22200002-2-2200000000000000000000-20200000
χ3122-2-2-22-2222-22-2-2-2-2220000-222-200000000000000000000020-20000
χ3222-2-2-22-2222-22-2-2-2-2220000-222-2000000000000000000000-2020000
χ3322-2-2-2-222-222222-2-2-2-222-2-2-2-22222-2-2-2-22200000000000000000000
χ3422-2-2-2-222-222222-2-2-2-2-2-222-2-222-2-22222-2-200000000000000000000
χ3522-2-2-2-22-1-222-1-1-1111122-2-211-1-1-1-11111-1-100003−3−333−3−3300000000
χ3622-2-2-2-22-1-222-1-1-1111122-2-211-1-1-1-11111-1-10000−333−3−333−300000000
χ3722-2-2-2-22-1-222-1-1-11111-2-22211-1-111-1-1-1-11100003−3−33−333−300000000
χ3822-2-2-2-22-1-222-1-1-11111-2-22211-1-111-1-1-1-1110000−333−33−3−3300000000
χ3944444-4-4-2-44-4-222-2-2220000-22-220000000000000000000000000000
χ404444-44-4-2-4-44-222-2-22200002-22-20000000000000000000000000000
χ4144-4-44-4-4-24-44-22222-2-20000-222-20000000000000000000000000000
χ4244-4-4-44-4-244-4-22222-2-200002-2-220000000000000000000000000000
χ434-44i−4i0004000-4004i−4i002-22i−2i00002-22i−2i2i−2i2-200000000000000000000
χ444-44i−4i0004000-4004i−4i00-22−2i2i0000-22−2i2i−2i2i-2200000000000000000000
χ454-44i−4i000-20002−2i32i3−2i2i23−232-22i−2i0000−1−i31+i32ζ11−2ζ112ζ7−2ζ7−1+i31−i300000000000000000000
χ464-44i−4i000-20002−2i32i3−2i2i23−23-22−2i2i00001+i3−1−i3−2ζ112ζ11−2ζ72ζ71−i3−1+i300000000000000000000
χ474-44i−4i000-200022i3−2i3−2i2i−23232-22i−2i0000−1+i31−i32ζ7−2ζ72ζ11−2ζ11−1−i31+i300000000000000000000
χ484-44i−4i000-200022i3−2i3−2i2i−2323-22−2i2i00001−i3−1+i3−2ζ72ζ7−2ζ112ζ111+i3−1−i300000000000000000000
χ494-4−4i4i0004000-400−4i4i002-2−2i2i00002-2−2i2i−2i2i2-200000000000000000000
χ504-4−4i4i0004000-400−4i4i00-222i−2i0000-222i−2i2i−2i-2200000000000000000000
χ514-4−4i4i000-20002−2i32i32i−2i−23232-2−2i2i0000−1−i31+i3−2ζ112ζ11−2ζ72ζ7−1+i31−i300000000000000000000
χ524-4−4i4i000-20002−2i32i32i−2i−2323-222i−2i00001+i3−1−i32ζ11−2ζ112ζ7−2ζ71−i3−1+i300000000000000000000
χ534-4−4i4i000-200022i3−2i32i−2i23−232-2−2i2i0000−1+i31−i3−2ζ72ζ7−2ζ112ζ11−1−i31+i300000000000000000000
χ544-4−4i4i000-200022i3−2i32i−2i23−23-222i−2i00001−i3−1+i32ζ7−2ζ72ζ11−2ζ111+i3−1−i300000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.