Finite Group Databasebeta

← Group #68340

Character table — Group #68340

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size1111222244444444488222244448888888881616333366661212121212121212122424
order12224444488888888243666121212121224242424242424246122222444448888888824
χ1111111111111111111111111111111111111111111111111111111111
χ21111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1
χ3111111111-1-1-1-11111-1-1111111111-1-1-1-11111-1-1111111111-1-1-1-11111-1-1
χ4111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111
χ51111-1-1-1-11ii−i−iii−i−i1-11111-1-1-1-11ii−i−iii−i−i1-11111-1-1-1-11ii−i−iii−i−i1-1
χ61111-1-1-1-11ii−i−i−i−iii-111111-1-1-1-11ii−i−i−i−iii-111111-1-1-1-11ii−i−i−i−iii-11
χ71111-1-1-1-11−i−iiiii−i−i-111111-1-1-1-11−i−iiiii−i−i-111111-1-1-1-11−i−iiiii−i−i-11
χ81111-1-1-1-11−i−iii−i−iii1-11111-1-1-1-11−i−iii−i−iii1-11111-1-1-1-11−i−iii−i−iii1-1
χ9222222-2-2-20000000000222222-2-2-20000000000222222-2-2-20000000000
χ102222-2-222-200000000002222-2-222-200000000002222-2-222-20000000000
χ1122-2-2002i−2i01+i−1−i1−i−1+i00000022-2-2002i−2i01+i−1−i1−i−1+i00000022-2-2002i−2i01+i−1−i1−i−1+i000000
χ1222-2-2002i−2i0−1−i1+i−1+i1−i00000022-2-2002i−2i0−1−i1+i−1+i1−i00000022-2-2002i−2i0−1−i1+i−1+i1−i000000
χ1322-2-200−2i2i01−i−1+i1+i−1−i00000022-2-200−2i2i01−i−1+i1+i−1−i00000022-2-200−2i2i01−i−1+i1+i−1−i000000
χ1422-2-200−2i2i0−1+i1−i−1−i1+i00000022-2-200−2i2i0−1+i1−i−1−i1+i00000022-2-200−2i2i0−1+i1−i−1−i1+i000000
χ152-22-22i−2i00000001+i−1−i1−i−1+i002-22-22i−2i00000001+i−1−i1−i−1+i002-22-22i−2i00000001+i−1−i1−i−1+i00
χ162-22-22i−2i0000000−1−i1+i−1+i1−i002-22-22i−2i0000000−1−i1+i−1+i1−i002-22-22i−2i0000000−1−i1+i−1+i1−i00
χ172-22-2−2i2i00000001−i−1+i1+i−1−i002-22-2−2i2i00000001−i−1+i1+i−1−i002-22-2−2i2i00000001−i−1+i1+i−1−i00
χ182-22-2−2i2i0000000−1+i1−i−1−i1+i002-22-2−2i2i0000000−1+i1−i−1−i1+i002-22-2−2i2i0000000−1+i1−i−1−i1+i00
χ194-4-440000000000000004-4-440000000000000004-4-44000000000000000
χ2011111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ211111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ22111111111-1-1-1-11111-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ23111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1
χ241111-1-1-1-11ii−i−iii−i−i1-11111-1-1-1-11ii−i−iii−i−i1-1-1-1-1-11111-1−i−iii−i−iii-11
χ251111-1-1-1-11ii−i−i−i−iii-111111-1-1-1-11ii−i−i−i−iii-11-1-1-1-11111-1−i−iiiii−i−i1-1
χ261111-1-1-1-11−i−iiiii−i−i-111111-1-1-1-11−i−iiiii−i−i-11-1-1-1-11111-1ii−i−i−i−iii1-1
χ271111-1-1-1-11−i−iii−i−iii1-11111-1-1-1-11−i−iii−i−iii1-1-1-1-1-11111-1ii−i−iii−i−i-11
χ28222222-2-2-20000000000222222-2-2-20000000000-2-2-2-2-2-22220000000000
χ292222-2-222-200000000002222-2-222-20000000000-2-2-2-222-2-220000000000
χ3022-2-2002i−2i01+i−1−i1−i−1+i00000022-2-2002i−2i01+i−1−i1−i−1+i000000-2-22200−2i2i0−1−i1+i−1+i1−i000000
χ3122-2-2002i−2i0−1−i1+i−1+i1−i00000022-2-2002i−2i0−1−i1+i−1+i1−i000000-2-22200−2i2i01+i−1−i1−i−1+i000000
χ3222-2-200−2i2i01−i−1+i1+i−1−i00000022-2-200−2i2i01−i−1+i1+i−1−i000000-2-222002i−2i0−1+i1−i−1−i1+i000000
χ3322-2-200−2i2i0−1+i1−i−1−i1+i00000022-2-200−2i2i0−1+i1−i−1−i1+i000000-2-222002i−2i01−i−1+i1+i−1−i000000
χ342-22-22i−2i00000001+i−1−i1−i−1+i002-22-22i−2i00000001+i−1−i1−i−1+i00-22-22−2i2i0000000−1−i1+i−1+i1−i00
χ352-22-22i−2i0000000−1−i1+i−1+i1−i002-22-22i−2i0000000−1−i1+i−1+i1−i00-22-22−2i2i00000001+i−1−i1−i−1+i00
χ362-22-2−2i2i00000001−i−1+i1+i−1−i002-22-2−2i2i00000001−i−1+i1+i−1−i00-22-222i−2i0000000−1+i1−i−1−i1+i00
χ372-22-2−2i2i0000000−1+i1−i−1−i1+i002-22-2−2i2i0000000−1+i1−i−1−i1+i00-22-222i−2i00000001−i−1+i1+i−1−i00
χ384-4-440000000000000004-4-44000000000000000-444-4000000000000000
χ392222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000
χ402222222222222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-11111110000000000000000000
χ41222222222-2-2-2-22222-2-2-1-1-1-1-1-1-1-1-11111-1-1-1-1110000000000000000000
χ42222222222-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-111111111-1-10000000000000000000
χ432222-2-2-2-222i2i−2i−2i2i2i−2i−2i2-2-1-1-1-11111-1−i−iii−i−iii-110000000000000000000
χ442222-2-2-2-222i2i−2i−2i−2i−2i2i2i-22-1-1-1-11111-1−i−iiiii−i−i1-10000000000000000000
χ452222-2-2-2-22−2i−2i2i2i2i2i−2i−2i-22-1-1-1-11111-1ii−i−i−i−iii1-10000000000000000000
χ462222-2-2-2-22−2i−2i2i2i−2i−2i2i2i2-2-1-1-1-11111-1ii−i−iii−i−i-110000000000000000000
χ47444444-4-4-40000000000-2-2-2-2-2-222200000000000000000000000000000
χ484444-4-444-40000000000-2-2-2-222-2-2200000000000000000000000000000
χ4944-4-4004i−4i02+2i−2−2i2−2i−2+2i000000-2-22200−2i2i0−1−i1+i−1+i1−i0000000000000000000000000
χ5044-4-4004i−4i0−2−2i2+2i−2+2i2−2i000000-2-22200−2i2i01+i−1−i1−i−1+i0000000000000000000000000
χ5144-4-400−4i4i02−2i−2+2i2+2i−2−2i000000-2-222002i−2i0−1+i1−i−1−i1+i0000000000000000000000000
χ5244-4-400−4i4i0−2+2i2−2i−2−2i2+2i000000-2-222002i−2i01−i−1+i1+i−1−i0000000000000000000000000
χ534-44-44i−4i00000002+2i−2−2i2−2i−2+2i00-22-22−2i2i0000000−1−i1+i−1+i1−i000000000000000000000
χ544-44-44i−4i0000000−2−2i2+2i−2+2i2−2i00-22-22−2i2i00000001+i−1−i1−i−1+i000000000000000000000
χ554-44-4−4i4i00000002−2i−2+2i2+2i−2−2i00-22-222i−2i0000000−1+i1−i−1−i1+i000000000000000000000
χ564-44-4−4i4i0000000−2+2i2−2i−2−2i2+2i00-22-222i−2i00000001−i−1+i1+i−1−i000000000000000000000
χ578-8-88000000000000000-444-40000000000000000000000000000000000

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