Finite Group Databasebeta

← Group #68277

Character table — Group #68277

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size1111222222223333444444444444466668888888888812121212121212121216162424
order122222344666444444444668888121244442412121212122424242444444888861224
χ1111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111-1-1-1-1111111-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111-1-1-1-1111111111111-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1
χ411111111111111111-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-11111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111-1-1
χ6111111111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-11111-1-111
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
χ8111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-11111111111-1-1
χ91111-1-11-1-111111111ii−i−i-1-1ii−i−i-1-1-1-1-1-11-11ii−i−iii−i−i1ii−i−iii−i−i1-1-11
χ101111-1-11-1-111111111ii−i−i-1-1−i−iii-1-1-1-1-1-1-111ii−i−i−i−iii1ii−i−i−i−iii-111-1
χ111111-1-11-1-111111111−i−iii-1-1ii−i−i-1-1-1-1-1-1-111−i−iiiii−i−i1−i−iiiii−i−i-111-1
χ121111-1-11-1-111111111−i−iii-1-1−i−iii-1-1-1-1-1-11-11−i−iii−i−iii1−i−iii−i−iii1-1-11
χ131111-1-11-1-1111-1-1-1-11ii−i−i-1-1ii−i−i-1-111111-11ii−i−iii−i−i-1−i−iii−i−iii1-11-1
χ141111-1-11-1-1111-1-1-1-11ii−i−i-1-1−i−iii-1-11111-111ii−i−i−i−iii-1−i−iiiii−i−i-11-11
χ151111-1-11-1-1111-1-1-1-11−i−iii-1-1ii−i−i-1-11111-111−i−iiiii−i−i-1ii−i−i−i−iii-11-11
χ161111-1-11-1-1111-1-1-1-11−i−iii-1-1−i−iii-1-111111-11−i−iii−i−iii-1ii−i−iii−i−i1-11-1
χ172222222-2-22222222-20000220000-2-2-2-22200-200000000-2000000000000
χ182222222-2-2222-2-2-2-2-20000220000-2-222-2-200-2000000002000000000000
χ19222222-122-1-1-1000022222-1-12222-1-1000022-1-1-1-1-1-1-1-1-1000000000-1-100
χ20222222-122-1-1-1000022222-1-1-2-2-2-2-1-10000-2-2-1-1-1-1-111110000000001100
χ21222222-122-1-1-100002-2-2-2-2-1-12222-1-10000-2-2-11111-1-1-1-10000000001100
χ22222222-122-1-1-100002-2-2-2-2-1-1-2-2-2-2-1-1000022-111111111000000000-1-100
χ232222-2-22222222222-20000-2-200002222-2-200-200000000-2000000000000
χ242222-2-2222222-2-2-2-2-20000-2-2000022-2-22200-2000000002000000000000
χ252222-2-2-1-2-2-1-1-1000022i2i−2i−2i112i2i−2i−2i1100002-2-1−i−iii−i−iii000000000-1100
χ262222-2-2-1-2-2-1-1-1000022i2i−2i−2i11−2i−2i2i2i110000-22-1−i−iiiii−i−i0000000001-100
χ272222-2-2-1-2-2-1-1-100002−2i−2i2i2i112i2i−2i−2i110000-22-1ii−i−i−i−iii0000000001-100
χ282222-2-2-1-2-2-1-1-100002−2i−2i2i2i11−2i−2i2i2i1100002-2-1ii−i−iii−i−i000000000-1100
χ292-22-20022i−2i2-2-22i2i−2i−2i01+i−1−i1−i−1+i0000002i−2i2-2000001+i−1−i1−i−1+i000001−i−1+i1+i−1−i00000000
χ302-22-20022i−2i2-2-22i2i−2i−2i0−1−i1+i−1+i1−i0000002i−2i2-200000−1−i1+i−1+i1−i00000−1+i1−i−1−i1+i00000000
χ312-22-20022i−2i2-2-2−2i−2i2i2i01+i−1−i1−i−1+i0000002i−2i-22000001+i−1−i1−i−1+i00000−1+i1−i−1−i1+i00000000
χ322-22-20022i−2i2-2-2−2i−2i2i2i0−1−i1+i−1+i1−i0000002i−2i-2200000−1−i1+i−1+i1−i000001−i−1+i1+i−1−i00000000
χ332-22-2002−2i2i2-2-22i2i−2i−2i01−i−1+i1+i−1−i000000−2i2i-22000001−i−1+i1+i−1−i00000−1−i1+i−1+i1−i00000000
χ342-22-2002−2i2i2-2-22i2i−2i−2i0−1+i1−i−1−i1+i000000−2i2i-2200000−1+i1−i−1−i1+i000001+i−1−i1−i−1+i00000000
χ352-22-2002−2i2i2-2-2−2i−2i2i2i01−i−1+i1+i−1−i000000−2i2i2-2000001−i−1+i1+i−1−i000001+i−1−i1−i−1+i00000000
χ362-22-2002−2i2i2-2-2−2i−2i2i2i0−1+i1−i−1−i1+i000000−2i2i2-200000−1+i1−i−1−i1+i00000−1−i1+i−1+i1−i00000000
χ372-2-222-2200-22-22-22-2000002-2i2−i2i2−i200002-20000000i2−i2i2−i200000i2−i2i2−i20000
χ382-2-222-2200-22-22-22-2000002-2−i2i2−i2i200002-20000000−i2i2−i2i200000−i2i2−i2i20000
χ392-2-222-2200-22-2-22-22000002-2i2−i2i2−i20000-220000000i2−i2i2−i200000−i2i2−i2i20000
χ402-2-222-2200-22-2-22-22000002-2−i2i2−i2i20000-220000000−i2i2−i2i200000i2−i2i2−i20000
χ412-2-22-22200-22-22-22-200000-222−2−220000-2200000002−2−22000002−2−220000
χ422-2-22-22200-22-22-22-200000-22−222−20000-220000000−222−200000−222−20000
χ432-2-22-22200-22-2-22-2200000-222−2−2200002-200000002−2−2200000−222−20000
χ442-2-22-22200-22-2-22-2200000-22−222−200002-20000000−222−2000002−2−220000
χ45444444-2-4-4-2-2-20000-40000-2-20000220000002000000000000000000000
χ464444-4-4-244-2-2-20000-40000220000-2-20000002000000000000000000000
χ4744-4-400400-4-444i−4i−4i4i00000000000000000000000000000000000000000
χ4844-4-400400-4-44−4i4i4i−4i00000000000000000000000000000000000000000
χ494-44-400-24i−4i-222000002+2i−2−2i2−2i−2+2i000000−2i2i0000000−1−i1+i−1+i1−i00000000000000000
χ504-44-400-24i−4i-22200000−2−2i2+2i−2+2i2−2i000000−2i2i00000001+i−1−i1−i−1+i00000000000000000
χ514-44-400-2−4i4i-222000002−2i−2+2i2+2i−2−2i0000002i−2i0000000−1+i1−i−1−i1+i00000000000000000
χ524-44-400-2−4i4i-22200000−2+2i2−2i−2−2i2+2i0000002i−2i00000001−i−1+i1+i−1−i00000000000000000
χ534-4-444-4-2002-22000000000-222i2−2i22i2−2i20000000000000−i2i2−i2i20000000000000
χ544-4-444-4-2002-22000000000-22−2i22i2−2i22i20000000000000i2−i2i2−i20000000000000
χ554-4-44-44-2002-220000000002-222−22−22220000000000000−222−20000000000000
χ564-4-44-44-2002-220000000002-2−222222−2200000000000002−2−220000000000000
χ5788-8-800-40044-4000000000000000000000000000000000000000000000

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