Finite Group Databasebeta

← Group #10705580

Character table — Group #10705580

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size111122222244444466668888888888888121212121616161616161616161616161616162424242424242424244848
order12222236664444664444488888888121212122244441212121212242424242424242428888888844
χ1111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-1-1-111111111-1-11-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1
χ3111111111111111111111-1-1-1-1111111111111-1-11-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1
χ4111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111
χ51111111111111111-1-1-1-11111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-11111-1-1-1-111
χ71111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1111111
χ81111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-111111111-1-1
χ91111111111-1-1-1-11111111ii−i−iii−i−i-1-1-1-1-1-1-1-11-1111-1-1ii−i−iii−i−i1ii−i−iii−i−i1-1
χ101111111111-1-1-1-11111111ii−i−i−i−iii-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i1−i−iiiii−i−i-11
χ111111111111-1-1-1-11111111−i−iiiii−i−i-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii1ii−i−i−i−iii-11
χ121111111111-1-1-1-11111111−i−iii−i−iii-1-1-1-1-1-1-1-11-1111-1-1−i−iii−i−iii1−i−iii−i−iii1-1
χ131111111111-1-1-1-111-1-1-1-11ii−i−iii−i−i-1-1-1-111111-1111-1-1ii−i−iii−i−i-1−i−iii−i−iii-11
χ141111111111-1-1-1-111-1-1-1-11ii−i−i−i−iii-1-1-1-11111-111-1-111−i−iiiii−i−i-1ii−i−i−i−iii1-1
χ151111111111-1-1-1-111-1-1-1-11−i−iiiii−i−i-1-1-1-11111-111-1-111ii−i−i−i−iii-1−i−iiiii−i−i1-1
χ161111111111-1-1-1-111-1-1-1-11−i−iii−i−iii-1-1-1-111111-1111-1-1−i−iii−i−iii-1ii−i−iii−i−i-11
χ1722222222222-2-22222222-2000000002-2-22-2-22200-2000000000000-20000000000
χ1822222222222-2-2222-2-2-2-2-2000000002-2-2222-2-200-200000000000020000000000
χ192222222222-222-2222222-200000000-222-222-2-200-2000000000000-20000000000
χ202222222222-222-222-2-2-2-2-200000000-222-2-2-22200-200000000000020000000000
χ21222222-1-1-1-12222-1-10000222222222-1-1-1-1000022-1-1-1-1-1-1-1-1-1-1-1-1-100000000000
χ22222222-1-1-1-12222-1-1000022222-2-2-2-2-1-1-1-10000-2-2-111111111-1-1-1-100000000000
χ23222222-1-1-1-12222-1-100002-2-2-2-22222-1-1-1-10000-2-2-11111-1-1-1-1111100000000000
χ24222222-1-1-1-12222-1-100002-2-2-2-2-2-2-2-2-1-1-1-1000022-1-1-1-1-11111111100000000000
χ25222222-1-1-1-1-2-2-2-2-1-1000022i2i−2i−2i2i2i−2i−2i111100002-2-1-1-111−i−iii−i−iii00000000000
χ26222222-1-1-1-1-2-2-2-2-1-1000022i2i−2i−2i−2i−2i2i2i11110000-22-111-1-1ii−i−i−i−iii00000000000
χ27222222-1-1-1-1-2-2-2-2-1-100002−2i−2i2i2i2i2i−2i−2i11110000-22-111-1-1−i−iiiii−i−i00000000000
χ28222222-1-1-1-1-2-2-2-2-1-100002−2i−2i2i2i−2i−2i2i2i111100002-2-1-1-111ii−i−iii−i−i00000000000
χ292-22-22-22-22-202i−2i0-222i2i−2i−2i01+i−1−i1−i−1+i000002i−2i02-200000000000001+i−1−i1−i−1+i000001−i−1+i1+i−1−i00
χ302-22-22-22-22-202i−2i0-222i2i−2i−2i0−1−i1+i−1+i1−i000002i−2i02-20000000000000−1−i1+i−1+i1−i00000−1+i1−i−1−i1+i00
χ312-22-22-22-22-202i−2i0-22−2i−2i2i2i01+i−1−i1−i−1+i000002i−2i0-2200000000000001+i−1−i1−i−1+i00000−1+i1−i−1−i1+i00
χ322-22-22-22-22-202i−2i0-22−2i−2i2i2i0−1−i1+i−1+i1−i000002i−2i0-220000000000000−1−i1+i−1+i1−i000001−i−1+i1+i−1−i00
χ332-22-22-22-22-20−2i2i0-222i2i−2i−2i01−i−1+i1+i−1−i00000−2i2i0-2200000000000001−i−1+i1+i−1−i00000−1−i1+i−1+i1−i00
χ342-22-22-22-22-20−2i2i0-222i2i−2i−2i0−1+i1−i−1−i1+i00000−2i2i0-220000000000000−1+i1−i−1−i1+i000001+i−1−i1−i−1+i00
χ352-22-22-22-22-20−2i2i0-22−2i−2i2i2i01−i−1+i1+i−1−i00000−2i2i02-200000000000001−i−1+i1+i−1−i000001+i−1−i1−i−1+i00
χ362-22-22-22-22-20−2i2i0-22−2i−2i2i2i0−1+i1−i−1−i1+i00000−2i2i02-20000000000000−1+i1−i−1−i1+i00000−1−i1+i−1+i1−i00
χ372-22-2-222-22-2200-22-22i−2i2i−2i00000−i2i2−i2i2-2002002i−2i0000000−i2i2−i2i2000002−22−2000000
χ382-22-2-222-22-2200-22-22i−2i2i−2i00000i2−i2i2−i2-2002002i−2i0000000i2−i2i2−i200000−22−22000000
χ392-22-2-222-22-2200-22-2−2i2i−2i2i00000−i2i2−i2i2-200200−2i2i0000000−i2i2−i2i200000−22−22000000
χ402-22-2-222-22-2200-22-2−2i2i−2i2i00000i2−i2i2−i2-200200−2i2i0000000i2−i2i2−i2000002−22−2000000
χ412-22-2-222-22-2-20022-22i−2i2i−2i000002−2−22200-200−2i2i00000002−2−2200000i2−i2−i2i2000000
χ422-22-2-222-22-2-20022-22i−2i2i−2i00000−222−2200-200−2i2i0000000−222−200000−i2i2i2−i2000000
χ432-22-2-222-22-2-20022-2−2i2i−2i2i000002−2−22200-2002i−2i00000002−2−2200000−i2i2i2−i2000000
χ442-22-2-222-22-2-20022-2−2i2i−2i2i00000−222−2200-2002i−2i0000000−222−200000i2−i2−i2i2000000
χ45444444-2-2-2-24-4-44-2-20000-400000000-222-2000000200000000000000000000000
χ46444444-2-2-2-2-444-4-2-20000-4000000002-2-22000000200000000000000000000000
χ474444-4-444440000-4-44-4-440000000000000000000000000000000000000000000
χ484444-4-444440000-4-4-444-40000000000000000000000000000000000000000000
χ494-44-44-4-22-2204i−4i02-2000002+2i−2−2i2−2i−2+2i00000−2i2i0000000000000000−1−i1+i−1+i1−i00000000000
χ504-44-44-4-22-2204i−4i02-200000−2−2i2+2i−2+2i2−2i00000−2i2i00000000000000001+i−1−i1−i−1+i00000000000
χ514-44-44-4-22-220−4i4i02-2000002−2i−2+2i2+2i−2−2i000002i−2i0000000000000000−1+i1−i−1−i1+i00000000000
χ524-44-44-4-22-220−4i4i02-200000−2+2i2−2i−2−2i2+2i000002i−2i00000000000000001−i−1+i1+i−1−i00000000000
χ534-44-4-44-22-22400-4-22000000000−2i22i2−2i22i2200-200000000000i2−i2i2−i2000000000000000
χ544-44-4-44-22-22400-4-220000000002i2−2i22i2−2i2200-200000000000−i2i2−i2i2000000000000000
χ554-44-4-44-22-22-4004-2200000000022−22−2222-200200000000000−222−2000000000000000
χ564-44-4-44-22-22-4004-22000000000−222222−22-2002000000000002−2−22000000000000000
χ578888-8-8-4-4-4-400004400000000000000000000000000000000000000000000000
χ5888-8-80088-8-800000000000000000000000000000000000000000000000000000
χ5988-8-800-4-44400000000000000000000000000000000−2i32i30000000000000000000
χ6088-8-800-4-444000000000000000000000000000000002i3−2i30000000000000000000
χ618-8-88008-8-8800000000000000000000000000000000000000000000000000000
χ628-8-8800-444-4000000000000000000000000000000−2i32i3000000000000000000000
χ638-8-8800-444-40000000000000000000000000000002i3−2i3000000000000000000000

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