Finite Group Databasebeta

← Group #10693113

Character table — Group #10693113

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444444444444444888888888888888888121212121616161616161616161624242424242448484848
order1222222236662222266666666664444444466121212121212121244444412121212121212122244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ41111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
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
χ7111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1
χ9111111-1-1111111-1-1-1111111-1-1-1-111-1-1ii−i−i-1-11111-1-1-1-111-1-1i−iii−i−iii−i−i1-1ii−i−i1-1i−i
χ10111111-1-1111111-1-1-1111111-1-1-1-111-1-1ii−i−i-1-11111-1-1-1-1-1-111i−iii−i−iii−i−i-11−i−iii-11−ii
χ11111111-1-1111111-1-1-1111111-1-1-1-111-1-1−i−iii-1-11111-1-1-1-111-1-1−ii−i−iii−i−iii1-1−i−iii1-1−ii
χ12111111-1-1111111-1-1-1111111-1-1-1-111-1-1−i−iii-1-11111-1-1-1-1-1-111−ii−i−iii−i−iii-11ii−i−i-11i−i
χ13111111-1-1111111-1-1-1111111-1-1-1-1-1-111ii−i−i-1-1-1-1-1-1111111-1-1−iiii−i−i−i−iii1-1ii−i−i-11−ii
χ14111111-1-1111111-1-1-1111111-1-1-1-1-1-111ii−i−i-1-1-1-1-1-11111-1-111−iiii−i−i−i−iii-11−i−iii1-1i−i
χ15111111-1-1111111-1-1-1111111-1-1-1-1-1-111−i−iii-1-1-1-1-1-1111111-1-1i−i−i−iiiii−i−i1-1−i−iii-11i−i
χ16111111-1-1111111-1-1-1111111-1-1-1-1-1-111−i−iii-1-1-1-1-1-11111-1-111i−i−i−iiiii−i−i-11ii−i−i1-1−ii
χ17222222222222-2-22-2-222-2-2-2-222-2-2000000002-20000000022220000000000-2-200000000
χ18222222222222-2-22-2-222-2-2-2-222-2-2000000002-200000000-2-2-2-200000000002200000000
χ1922222222-1-1-1-122222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-10000000000
χ2022222222-1-1-1-122222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-10000-2-2111111110000000000
χ2122222222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1111111110000-2-2-1-1-1-111110000000000
χ2222222222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000221111-1-1-1-10000000000
χ23222222-2-22222-2-2-22222-2-2-2-2-2-22200000000-220000000022-2-20000000000-2200000000
χ24222222-2-22222-2-2-22222-2-2-2-2-2-22200000000-2200000000-2-22200000000002-200000000
χ25222222-2-2-1-1-1-122-2-2-2-1-1-1-1-1-1111122-2-22i2i−2i−2i11-1-1-1-1111100002i−2i−i−iii−i−iii0000000000
χ26222222-2-2-1-1-1-122-2-2-2-1-1-1-1-1-1111122-2-2−2i−2i2i2i11-1-1-1-111110000−2i2iii−i−iii−i−i0000000000
χ27222222-2-2-1-1-1-122-2-2-2-1-1-1-1-1-11111-2-2222i2i−2i−2i111111-1-1-1-10000−2i2i−i−iiiii−i−i0000000000
χ28222222-2-2-1-1-1-122-2-2-2-1-1-1-1-1-11111-2-222−2i−2i2i2i111111-1-1-1-100002i−2iii−i−i−i−iii0000000000
χ292222-2-22222222-2-22-2-2-222-2-2222200002-22-2-2-2000000000000002-22-200000000000000
χ302222-2-22222222-2-22-2-2-222-2-222220000-22-22-2-200000000000000-22-2200000000000000
χ312222-2-2222222-22-2-22-2-2-2-22222-2-200000000-220000000000000000000000002-22-20000
χ322222-2-2222222-22-2-22-2-2-2-22222-2-200000000-22000000000000000000000000-22-220000
χ332222-2-222-1-1-1-12-2-22-211-1-111-1-1-1-100002-22-211−i3−i3i3i3−i3−i3i3i3000000-11-11−i3i3−i3i30000000000
χ342222-2-222-1-1-1-12-2-22-211-1-111-1-1-1-100002-22-211i3i3−i3−i3i3i3−i3−i3000000-11-11i3−i3i3−i30000000000
χ352222-2-222-1-1-1-12-2-22-211-1-111-1-1-1-10000-22-2211−i3−i3i3i3−i3−i3i3i30000001-11-1i3−i3i3−i30000000000
χ362222-2-222-1-1-1-12-2-22-211-1-111-1-1-1-10000-22-2211i3i3−i3−i3i3i3−i3−i30000001-11-1−i3i3−i3i30000000000
χ372222-2-2-2-222222-22-22-2-222-2-2-2-2-2-200002i−2i−2i2i22000000000000002i−2i−2i2i00000000000000
χ382222-2-2-2-222222-22-22-2-222-2-2-2-2-2-20000−2i2i2i−2i2200000000000000−2i2i2i−2i00000000000000
χ392222-2-2-2-22222-2222-2-2-2-2-222-2-222000000002-20000000000000000000000002i−2i−2i2i0000
χ402222-2-2-2-22222-2222-2-2-2-2-222-2-222000000002-2000000000000000000000000−2i2i2i−2i0000
χ412222-2-2-2-2-1-1-1-12-22-2211-1-111111100002i−2i−2i2i-1-1−i3−i3i3i3i3i3−i3−i3000000−iii−i3−3−330000000000
χ422222-2-2-2-2-1-1-1-12-22-2211-1-111111100002i−2i−2i2i-1-1i3i3−i3−i3−i3−i3i3i3000000−iii−i−333−30000000000
χ432222-2-2-2-2-1-1-1-12-22-2211-1-11111110000−2i2i2i−2i-1-1−i3−i3i3i3i3i3−i3−i3000000i−i−ii−333−30000000000
χ442222-2-2-2-2-1-1-1-12-22-2211-1-11111110000−2i2i2i−2i-1-1i3i3−i3−i3−i3−i3i3i3000000i−i−ii3−3−330000000000
χ4544444444-2-2-2-2-4-44-4-4-2-22222-2-22200000000-2200000000000000000000000000000000
χ46444444-4-4-2-2-2-2-4-4-444-2-2222222-2-2000000002-200000000000000000000000000000000
χ474444-4-444-2-2-2-2-44-4-442222-2-2-2-222000000002-200000000000000000000000000000000
χ484444-4-4-4-4-2-2-2-2-4444-42222-2-222-2-200000000-2200000000000000000000000000000000
χ4944-4-4004-444-4-4000000000004-4002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ5044-4-4004-444-4-4000000000004-400−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ5144-4-4004-4-2-2220000000−2i32i300-22−2i32i32i−2i2i−2i0000002ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ11000000000000000000000000
χ5244-4-4004-4-2-2220000000−2i32i300-22−2i32i3−2i2i−2i2i000000−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11000000000000000000000000
χ5344-4-4004-4-2-22200000002i3−2i300-222i3−2i32i−2i2i−2i0000002ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ7000000000000000000000000
χ5444-4-4004-4-2-22200000002i3−2i300-222i3−2i3−2i2i−2i2i000000−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7000000000000000000000000
χ5544-4-400-4444-4-400000000000-44002i−2i−2i2i0000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ5644-4-400-4444-4-400000000000-4400−2i2i2i−2i000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ5744-4-400-44-2-2220000000−2i32i3002-22i3−2i32i−2i−2i2i0000002ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ11000000000000000000000000
χ5844-4-400-44-2-2220000000−2i32i3002-22i3−2i3−2i2i2i−2i000000−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ11000000000000000000000000
χ5944-4-400-44-2-22200000002i3−2i3002-2−2i32i32i−2i−2i2i0000002ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ7000000000000000000000000
χ6044-4-400-44-2-22200000002i3−2i3002-2−2i32i3−2i2i2i−2i000000−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ7000000000000000000000000
χ614-4-444-4004-44-4000004-400000000000000000000000000004-400000000000000000000
χ624-4-444-4004-44-4000004-40000000000000000000000000000-4400000000000000000000
χ634-4-44-44004-44-400000-44000000000000000000000000004-40000000000000000000000
χ644-4-44-44004-44-400000-4400000000000000000000000000-440000000000000000000000
χ658-88-800008-8-88000000000000000000000000000000000000000000000000000000000
χ668-88-80000-444-4000000000−4i34i30000000000000000000000000000000000000000000000
χ678-88-80000-444-40000000004i3−4i30000000000000000000000000000000000000000000000
χ688-8-888-800-44-4400000-4400000000000000000000000000000000000000000000000000
χ698-8-88-8800-44-44000004-400000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.