Finite Group Databasebeta

← Group #68342

Character table — Group #68342

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size1111222222223333444444444444466668888888888812121212121212121216162424
order12223444466644444888888881212121244442412242424242424242428888888861224
χ1111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111-1-1-1-111111111-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111-1-1-1-1111111111111-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1
χ411111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-11111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111-1-1
χ6111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-11-1-1-1-11111-11111-1-1-1-1-1-111
χ8111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1-1-1-11111111111-1-1
χ911111-1-1-1-111111111ii−i−iii−i−i-1-1-1-1-1-1-1-11-11ii−i−iii−i−i1ii−i−iii−i−i1-1-11
χ1011111-1-1-1-111111111ii−i−i−i−iii-1-1-1-1-1-1-1-1-111ii−i−i−i−iii1ii−i−i−i−iii-111-1
χ1111111-1-1-1-111111111−i−iiiii−i−i-1-1-1-1-1-1-1-1-111−i−iiiii−i−i1−i−iiiii−i−i-111-1
χ1211111-1-1-1-111111111−i−iii−i−iii-1-1-1-1-1-1-1-11-11−i−iii−i−iii1−i−iii−i−iii1-1-11
χ1311111-1-1-1-1111-1-1-1-11ii−i−iii−i−i-1-1-1-111111-11ii−i−iii−i−i-1−i−iii−i−iii1-11-1
χ1411111-1-1-1-1111-1-1-1-11ii−i−i−i−iii-1-1-1-11111-111ii−i−i−i−iii-1−i−iiiii−i−i-11-11
χ1511111-1-1-1-1111-1-1-1-11−i−iiiii−i−i-1-1-1-11111-111−i−iiiii−i−i-1ii−i−i−i−iii-11-11
χ1611111-1-1-1-1111-1-1-1-11−i−iii−i−iii-1-1-1-111111-11−i−iii−i−iii-1ii−i−iii−i−i1-11-1
χ172222222-2-22222222-20000000022-2-222-2-200-200000000-2000000000000
χ182222222-2-2222-2-2-2-2-20000000022-2-2-2-22200-2000000002000000000000
χ1922222-2-2222222222-200000000-2-222-2-22200-200000000-2000000000000
χ2022222-2-222222-2-2-2-2-200000000-2-22222-2-200-2000000002000000000000
χ212222-12222-1-1-10000222222222-1-1-1-1000022-1-1-1-1-1-1-1-1-1000000000-1-100
χ222222-12222-1-1-1000022222-2-2-2-2-1-1-1-10000-2-2-1-1-1-1-111110000000001100
χ232222-12222-1-1-100002-2-2-2-22222-1-1-1-10000-2-2-11111-1-1-1-10000000001100
χ242222-12222-1-1-100002-2-2-2-2-2-2-2-2-1-1-1-1000022-111111111000000000-1-100
χ252222-1-2-2-2-2-1-1-1000022i2i−2i−2i2i2i−2i−2i111100002-2-1−i−iii−i−iii000000000-1100
χ262222-1-2-2-2-2-1-1-1000022i2i−2i−2i−2i−2i2i2i11110000-22-1−i−iiiii−i−i0000000001-100
χ272222-1-2-2-2-2-1-1-100002−2i−2i2i2i2i2i−2i−2i11110000-22-1ii−i−i−i−iii0000000001-100
χ282222-1-2-2-2-2-1-1-100002−2i−2i2i2i−2i−2i2i2i111100002-2-1ii−i−iii−i−i000000000-1100
χ2922-2-22002i−2i2-2-22i2i−2i−2i01+i−1−i1−i−1+i0000002i−2i002-20001+i−1−i1−i−1+i000001−i−1+i1+i−1−i00000000
χ3022-2-22002i−2i2-2-22i2i−2i−2i0−1−i1+i−1+i1−i0000002i−2i002-2000−1−i1+i−1+i1−i00000−1+i1−i−1−i1+i00000000
χ3122-2-22002i−2i2-2-2−2i−2i2i2i01+i−1−i1−i−1+i0000002i−2i00-220001+i−1−i1−i−1+i00000−1+i1−i−1−i1+i00000000
χ3222-2-22002i−2i2-2-2−2i−2i2i2i0−1−i1+i−1+i1−i0000002i−2i00-22000−1−i1+i−1+i1−i000001−i−1+i1+i−1−i00000000
χ3322-2-2200−2i2i2-2-22i2i−2i−2i01−i−1+i1+i−1−i000000−2i2i00-220001−i−1+i1+i−1−i00000−1−i1+i−1+i1−i00000000
χ3422-2-2200−2i2i2-2-22i2i−2i−2i0−1+i1−i−1−i1+i000000−2i2i00-22000−1+i1−i−1−i1+i000001+i−1−i1−i−1+i00000000
χ3522-2-2200−2i2i2-2-2−2i−2i2i2i01−i−1+i1+i−1−i000000−2i2i002-20001−i−1+i1+i−1−i000001+i−1−i1−i−1+i00000000
χ3622-2-2200−2i2i2-2-2−2i−2i2i2i0−1+i1−i−1−i1+i000000−2i2i002-2000−1+i1−i−1−i1+i00000−1−i1+i−1+i1−i00000000
χ372-22-222i−2i00-22-22i−2i2i−2i000001+i−1−i1−i−1+i2i−2i002-20000000001+i−1−i1−i−1+i000001−i−1+i1+i−1−i0000
χ382-22-222i−2i00-22-22i−2i2i−2i00000−1−i1+i−1+i1−i2i−2i002-2000000000−1−i1+i−1+i1−i00000−1+i1−i−1−i1+i0000
χ392-22-222i−2i00-22-2−2i2i−2i2i000001+i−1−i1−i−1+i2i−2i00-220000000001+i−1−i1−i−1+i00000−1+i1−i−1−i1+i0000
χ402-22-222i−2i00-22-2−2i2i−2i2i00000−1−i1+i−1+i1−i2i−2i00-22000000000−1−i1+i−1+i1−i000001−i−1+i1+i−1−i0000
χ412-22-22−2i2i00-22-22i−2i2i−2i000001−i−1+i1+i−1−i−2i2i00-220000000001−i−1+i1+i−1−i00000−1−i1+i−1+i1−i0000
χ422-22-22−2i2i00-22-22i−2i2i−2i00000−1+i1−i−1−i1+i−2i2i00-22000000000−1+i1−i−1−i1+i000001+i−1−i1−i−1+i0000
χ432-22-22−2i2i00-22-2−2i2i−2i2i000001−i−1+i1+i−1−i−2i2i002-20000000001−i−1+i1+i−1−i000001+i−1−i1−i−1+i0000
χ442-22-22−2i2i00-22-2−2i2i−2i2i00000−1+i1−i−1−i1+i−2i2i002-2000000000−1+i1−i−1−i1+i00000−1−i1+i−1+i1−i0000
χ454444-244-4-4-2-2-20000-400000000-2-2220000002000000000000000000000
χ464444-2-4-444-2-2-20000-40000000022-2-20000002000000000000000000000
χ4744-4-4-2004i−4i-222000002+2i−2−2i2−2i−2+2i000000−2i2i0000000−1−i1+i−1+i1−i00000000000000000
χ4844-4-4-2004i−4i-22200000−2−2i2+2i−2+2i2−2i000000−2i2i00000001+i−1−i1−i−1+i00000000000000000
χ4944-4-4-200−4i4i-222000002−2i−2+2i2+2i−2−2i0000002i−2i0000000−1+i1−i−1−i1+i00000000000000000
χ5044-4-4-200−4i4i-22200000−2+2i2−2i−2−2i2+2i0000002i−2i00000001−i−1+i1+i−1−i00000000000000000
χ514-44-4-24i−4i002-220000000002+2i−2−2i2−2i−2+2i−2i2i0000000000000−1−i1+i−1+i1−i0000000000000
χ524-44-4-24i−4i002-22000000000−2−2i2+2i−2+2i2−2i−2i2i00000000000001+i−1−i1−i−1+i0000000000000
χ534-44-4-2−4i4i002-220000000002−2i−2+2i2+2i−2−2i2i−2i0000000000000−1+i1−i−1−i1+i0000000000000
χ544-44-4-2−4i4i002-22000000000−2+2i2−2i−2−2i2+2i2i−2i00000000000001−i−1+i1+i−1−i0000000000000
χ554-4-4440000-4-444-4-4400000000000000000000000000000000000000000
χ564-4-4440000-4-44-444-400000000000000000000000000000000000000000
χ578-8-88-4000044-4000000000000000000000000000000000000000000000

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