Finite Group Databasebeta

← Group #10693209

Character table — Group #10693209

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444444444444444888888888888888888121212121616161616161616161624242424242448484848
order1222223446662244466666612121212444488881212121212121212121288888824242424242424242444884488
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1
χ91111-1-11-1-11111-11-1111-1-1-1-1-1-1-1-111-1-1ii−i−i111111-1-1-1-1ii−i−ii−iii−i−iii−i−i11-1-1i−ii−i1-1
χ101111-1-11-1-11111-11-1111-1-1-1-1-1-1-1-111-1-1ii−i−i111111-1-1-1-1−i−iiii−iii−i−iii−i−i-1-111−ii−ii-11
χ111111-1-11-1-11111-11-1111-1-1-1-1-1-1-1-111-1-1−i−iii111111-1-1-1-1ii−i−i−ii−i−iii−i−iii-1-111i−ii−i-11
χ121111-1-11-1-11111-11-1111-1-1-1-1-1-1-1-111-1-1−i−iii111111-1-1-1-1−i−iii−ii−i−iii−i−iii11-1-1−ii−ii1-1
χ131111-1-11-1-11111-11-1111-1-1-1-1-1-1-1-1-1-111ii−i−i11-1-1-1-11111ii−i−i−iiii−i−i−i−iii11-1-1i−i−ii-11
χ141111-1-11-1-11111-11-1111-1-1-1-1-1-1-1-1-1-111ii−i−i11-1-1-1-11111−i−iii−iiii−i−i−i−iii-1-111−iii−i1-1
χ151111-1-11-1-11111-11-1111-1-1-1-1-1-1-1-1-1-111−i−iii11-1-1-1-11111ii−i−ii−i−i−iiiii−i−i-1-111i−i−ii1-1
χ161111-1-11-1-11111-11-1111-1-1-1-1-1-1-1-1-1-111−i−iii11-1-1-1-11111−i−iiii−i−i−iiiii−i−i11-1-1−iii−i-11
χ17222222222222-2-22-2-2-2-222-2-222-2-2000000002-200000000222200000000000000-2-20000
χ18222222222222-2-22-2-2-2-222-2-222-2-2000000002-200000000-2-2-2-200000000000000220000
χ192222222-2-222222-2-2-2222222-2-2-2-200002i−2i2i−2i-2-2000000000000002i−2i2i−2i00000000000000
χ202222222-2-222222-2-2-2222222-2-2-2-20000−2i2i−2i2i-2-200000000000000−2i2i−2i2i00000000000000
χ212222222-2-2222-2-2-222-2-222-2-2-2-22200000000-2200000000000000000000002-22-2000000
χ222222222-2-2222-2-2-222-2-222-2-2-2-22200000000-220000000000000000000000-22-22000000
χ23222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-10000000000
χ24222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-10000-2-2111111110000000000
χ25222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1111111110000-2-2-1-1-1-111110000000000
χ26222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000221111-1-1-1-10000000000
χ27222222-1-2-2-1-1-122-2-2-2-1-1-1-1-1-1111100002i−2i2i−2i11−i3−i3i3i3−i3−i3i3i3000000−ii−ii3−33−30000000000
χ28222222-1-2-2-1-1-122-2-2-2-1-1-1-1-1-1111100002i−2i2i−2i11i3i3−i3−i3i3i3−i3−i3000000−ii−ii−33−330000000000
χ29222222-1-2-2-1-1-122-2-2-2-1-1-1-1-1-111110000−2i2i−2i2i11−i3−i3i3i3−i3−i3i3i3000000i−ii−i−33−330000000000
χ30222222-1-2-2-1-1-122-2-2-2-1-1-1-1-1-111110000−2i2i−2i2i11i3i3−i3−i3i3i3−i3−i3000000i−ii−i3−33−30000000000
χ312222-2-22222222-2-22-222-2-2-2-2222200002-2-22-2-2000000000000002-2-2200000000000000
χ322222-2-22222222-2-22-222-2-2-2-222220000-222-2-2-200000000000000-222-200000000000000
χ332222-2-2222222-22-2-22-2-2-2-22222-2-200000000-2200000000000000000000002-2-22000000
χ342222-2-2222222-22-2-22-2-2-2-22222-2-200000000-220000000000000000000000-222-2000000
χ352222-2-22-2-2222-2222-2-2-2-2-222-2-222000000002-2000000002i2i−2i−2i00000000000000−2i2i0000
χ362222-2-22-2-2222-2222-2-2-2-2-222-2-222000000002-200000000−2i−2i2i2i000000000000002i−2i0000
χ372222-2-2-122-1-1-12-2-22-2-1-11111-1-1-1-100002-2-2211−i3−i3i3i3i3i3−i3−i3000000-111-1−i3i3i3−i30000000000
χ382222-2-2-122-1-1-12-2-22-2-1-11111-1-1-1-100002-2-2211i3i3−i3−i3−i3−i3i3i3000000-111-1i3−i3−i3i30000000000
χ392222-2-2-122-1-1-12-2-22-2-1-11111-1-1-1-10000-222-211−i3−i3i3i3i3i3−i3−i30000001-1-11i3−i3−i3i30000000000
χ402222-2-2-122-1-1-12-2-22-2-1-11111-1-1-1-10000-222-211i3i3−i3−i3−i3−i3i3i30000001-1-11−i3i3i3−i30000000000
χ412222-2-2-1-2-2-1-1-12-22-22-1-11111111122-2-22i2i−2i−2i-1-1-1-1-1-1111100002i−2i−i−iii−i−iii0000000000
χ422222-2-2-1-2-2-1-1-12-22-22-1-11111111122-2-2−2i−2i2i2i-1-1-1-1-1-111110000−2i2iii−i−iii−i−i0000000000
χ432222-2-2-1-2-2-1-1-12-22-22-1-111111111-2-2222i2i−2i−2i-1-11111-1-1-1-10000−2i2i−i−iiiii−i−i0000000000
χ442222-2-2-1-2-2-1-1-12-22-22-1-111111111-2-222−2i−2i2i2i-1-11111-1-1-1-100002i−2iii−i−i−i−iii0000000000
χ45444444-244-2-2-2-4-44-4-422-2-222-2-22200000000-2200000000000000000000000000000000
χ46444444-2-4-4-2-2-2-4-4-44422-2-22222-2-2000000002-200000000000000000000000000000000
χ474444-4-4-244-2-2-2-44-4-442222-2-2-2-222000000002-200000000000000000000000000000000
χ484444-4-4-2-4-4-2-2-2-4444-42222-2-222-2-200000000-2200000000000000000000000000000000
χ4944-4-44-44004-4-400000004-400000000000000000000000022−2222−2200000000000000000000
χ5044-4-44-44004-4-400000004-4000000000000000000000000−2222−222200000000000000000000
χ5144-4-4-444004-4-40000000-44000000000000000000000000−2i22i22i2−2i200000000000000000000
χ5244-4-4-444004-4-40000000-440000000000000000000000002i2−2i2−2i22i200000000000000000000
χ534-4-440044-4-4-44000000000004-4002-22-20000002-22-22-22-2000000000000000000000000
χ544-4-440044-4-4-44000000000004-400-22-22000000-22-22-22-22000000000000000000000000
χ554-4-44004-44-4-4400000000000-44002-2-220000002-22-2-22-22000000000000000000000000
χ564-4-44004-44-4-4400000000000-4400-222-2000000-22-222-22-2000000000000000000000000
χ574-4-4400-24-422-200000−2i32i30000-22−2i32i32-22-2000000−1−i31+i3−1+i31−i3−1+i31−i3−1−i31+i3000000000000000000000000
χ584-4-4400-24-422-200000−2i32i30000-22−2i32i3-22-220000001+i3−1−i31−i3−1+i31−i3−1+i31+i3−1−i3000000000000000000000000
χ594-4-4400-24-422-2000002i3−2i30000-222i3−2i32-22-2000000−1+i31−i3−1−i31+i3−1−i31+i3−1+i31−i3000000000000000000000000
χ604-4-4400-24-422-2000002i3−2i30000-222i3−2i3-22-220000001−i3−1+i31+i3−1−i31+i3−1−i31−i3−1+i3000000000000000000000000
χ614-4-4400-2-4422-200000−2i32i300002-22i3−2i32-2-22000000−1−i31+i3−1+i31−i31−i3−1+i31+i3−1−i3000000000000000000000000
χ624-4-4400-2-4422-200000−2i32i300002-22i3−2i3-222-20000001+i3−1−i31−i3−1+i3−1+i31−i3−1−i31+i3000000000000000000000000
χ634-4-4400-2-4422-2000002i3−2i300002-2−2i32i32-2-22000000−1+i31−i3−1−i31+i31+i3−1−i31−i3−1+i3000000000000000000000000
χ644-4-4400-2-4422-2000002i3−2i300002-2−2i32i3-222-20000001−i3−1+i31+i3−1−i3−1−i31+i3−1+i31−i3000000000000000000000000
χ6588-8-88-8-400-4440000000-44000000000000000000000000000000000000000000000000
χ6688-8-8-88-400-44400000004-4000000000000000000000000000000000000000000000000
χ678-88-800800-88-8000000000000000000000000000000000000000000000000000000000
χ688-88-800-4004-44000000000−4i34i30000000000000000000000000000000000000000000000
χ698-88-800-4004-440000000004i3−4i30000000000000000000000000000000000000000000000

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