Finite Group Databasebeta

← Group #10698426

Character table — Group #10698426

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888888888888888816161616161624242424484848484848
order1222223444466666662244121212121212121244444444661212121212121212121212121212121244121212122244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ6111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111
χ9222222222-2-22222222-2-22-22222-2-2-2-2000022-2-2-2-2000000002222-2-2-2-20000000000000000
χ10222222222-2-22222222-2-22-22222-2-2-2-20000-2-222-2-200000000-2-2-2-222220000000000000000
χ112222222-2-2222222222-2-2-22-2-2-2-2222222-2-20000-2-22222-2-2-2-2000000000000000000000000
χ122222222-2-2222222222-2-2-22-2-2-2-22222-2-2220000-2-2-2-2-2-22222000000000000000000000000
χ132222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2000000002200000000000000002-222-2-20000000000
χ142222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-200000000220000000000000000-22-2-2220000000000
χ15222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000000000
χ16222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-211110000000000
χ17222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-211110000000000
χ18222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-10000000000
χ19222222-122-2-2-1-1-1-1-1-1-1-2-22-2-1-1-1-11111000022-2-211−i3−i3i3i3−i3−i3i3i3-1-1-1-1111100−i3i3−i3i30000000000
χ20222222-122-2-2-1-1-1-1-1-1-1-2-22-2-1-1-1-11111000022-2-211i3i3−i3−i3i3i3−i3−i3-1-1-1-1111100i3−i3i3−i30000000000
χ21222222-122-2-2-1-1-1-1-1-1-1-2-22-2-1-1-1-111110000-2-22211−i3−i3i3i3−i3−i3i3i31111-1-1-1-100i3−i3i3−i30000000000
χ22222222-122-2-2-1-1-1-1-1-1-1-2-22-2-1-1-1-111110000-2-22211i3i3−i3−i3i3i3−i3−i31111-1-1-1-100−i3i3−i3i30000000000
χ23222222-1-2-222-1-1-1-1-1-1-1-2-2-221111-1-1-1-122-2-2000011-1-1-1-11111−i3−i3i3i3−i3−i3i3i300−i3i3i3−i30000000000
χ24222222-1-2-222-1-1-1-1-1-1-1-2-2-221111-1-1-1-122-2-2000011-1-1-1-11111i3i3−i3−i3i3i3−i3−i300i3−i3−i3i30000000000
χ25222222-1-2-222-1-1-1-1-1-1-1-2-2-221111-1-1-1-1-2-2220000111111-1-1-1-1−i3−i3i3i3−i3−i3i3i300i3−i3−i3i30000000000
χ26222222-1-2-222-1-1-1-1-1-1-1-2-2-221111-1-1-1-1-2-2220000111111-1-1-1-1i3i3−i3−i3i3i3−i3−i300−i3i3i3−i30000000000
χ27222222-1-2-2-2-2-1-1-1-1-1-1-122-2-21111111100000000-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i32-2-1-1110000000000
χ28222222-1-2-2-2-2-1-1-1-1-1-1-122-2-21111111100000000-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3-2211-1-10000000000
χ29222222-1-2-2-2-2-1-1-1-1-1-1-122-2-21111111100000000-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3-2211-1-10000000000
χ30222222-1-2-2-2-2-1-1-1-1-1-1-122-2-21111111100000000-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i32-2-1-1110000000000
χ312222-2-222222222-2-2-2-22-2-2-222-2-222-2-2000000002-2000000000000000000000000002i−2i0000
χ322222-2-222222222-2-2-2-22-2-2-222-2-222-2-2000000002-200000000000000000000000000−2i2i0000
χ332222-2-2222-2-2222-2-2-2-2-22-2222-2-2-2-22200000000-2200000000000000000000000000002i−2i00
χ342222-2-2222-2-2222-2-2-2-2-22-2222-2-2-2-22200000000-220000000000000000000000000000−2i2i00
χ352222-2-22-2-222222-2-2-2-2-222-2-2-22222-2-200000000-220000000000000000000000000000002i−2i
χ362222-2-22-2-222222-2-2-2-2-222-2-2-22222-2-200000000-22000000000000000000000000000000−2i2i
χ372222-2-22-2-2-2-2222-2-2-2-22-222-2-222-2-222000000002-2000000000000000000000022-2-2000000
χ382222-2-22-2-2-2-2222-2-2-2-22-222-2-222-2-222000000002-20000000000000000000000-2-222000000
χ394444-4-4-24444-2-2-222224-4-4-4-2-222-2-22200000000-2200000000000000000000000000000000
χ404444-4-4-244-4-4-2-2-22222-44-44-2-22222-2-2000000002-200000000000000000000000000000000
χ414444-4-4-2-4-444-2-2-22222-444-422-2-2-2-222000000002-200000000000000000000000000000000
χ424444-4-4-2-4-4-4-4-2-2-222224-44422-2-222-2-200000000-2200000000000000000000000000000000
χ4344-4-4004004i−4i4-4-40000000000004i−4i0000002-22i−2i00000000002-22-22i−2i2i−2i0000000000000000
χ4444-4-4004004i−4i4-4-40000000000004i−4i000000-22−2i2i0000000000-22-22−2i2i−2i2i0000000000000000
χ4544-4-400400−4i4i4-4-4000000000000−4i4i0000002-2−2i2i00000000002-22-2−2i2i−2i2i0000000000000000
χ4644-4-400400−4i4i4-4-4000000000000−4i4i000000-222i−2i0000000000-22-222i−2i2i−2i0000000000000000
χ4744-4-400-2004i−4i-222−2i3−2i32i32i300000000−2i2i23−2300002-22i−2i0000000000−1−i31+i3−1+i31−i32ζ11−2ζ112ζ7−2ζ70000000000000000
χ4844-4-400-2004i−4i-222−2i3−2i32i32i300000000−2i2i23−230000-22−2i2i00000000001+i3−1−i31−i3−1+i3−2ζ112ζ11−2ζ72ζ70000000000000000
χ4944-4-400-2004i−4i-2222i32i3−2i3−2i300000000−2i2i−232300002-22i−2i0000000000−1+i31−i3−1−i31+i32ζ7−2ζ72ζ11−2ζ110000000000000000
χ5044-4-400-2004i−4i-2222i32i3−2i3−2i300000000−2i2i−23230000-22−2i2i00000000001−i3−1+i31+i3−1−i3−2ζ72ζ7−2ζ112ζ110000000000000000
χ5144-4-400-200−4i4i-222−2i3−2i32i32i3000000002i−2i−232300002-2−2i2i0000000000−1−i31+i3−1+i31−i3−2ζ112ζ11−2ζ72ζ70000000000000000
χ5244-4-400-200−4i4i-222−2i3−2i32i32i3000000002i−2i−23230000-222i−2i00000000001+i3−1−i31−i3−1+i32ζ11−2ζ112ζ7−2ζ70000000000000000
χ5344-4-400-200−4i4i-2222i32i3−2i3−2i3000000002i−2i23−2300002-2−2i2i0000000000−1+i31−i3−1−i31+i3−2ζ72ζ7−2ζ112ζ110000000000000000
χ5444-4-400-200−4i4i-2222i32i3−2i3−2i3000000002i−2i23−230000-222i−2i00000000001−i3−1+i31+i3−1−i32ζ7−2ζ72ζ11−2ζ110000000000000000
χ554-44-40044i−4i00-44-4000000004i−4i0000002-22i−2i0000002-22-22i−2i2i−2i000000000000000000000000
χ564-44-40044i−4i00-44-4000000004i−4i000000-22−2i2i000000-22-22−2i2i−2i2i000000000000000000000000
χ574-44-4004−4i4i00-44-400000000−4i4i0000002-2−2i2i0000002-22-2−2i2i−2i2i000000000000000000000000
χ584-44-4004−4i4i00-44-400000000−4i4i000000-222i−2i000000-22-222i−2i2i−2i000000000000000000000000
χ594-44-400-24i−4i002-22−2i32i3−2i32i30000−2i2i23−2300002-22i−2i000000−1−i31+i3−1+i31−i32ζ11−2ζ112ζ7−2ζ7000000000000000000000000
χ604-44-400-24i−4i002-22−2i32i3−2i32i30000−2i2i23−230000-22−2i2i0000001+i3−1−i31−i3−1+i3−2ζ112ζ11−2ζ72ζ7000000000000000000000000
χ614-44-400-24i−4i002-222i3−2i32i3−2i30000−2i2i−232300002-22i−2i000000−1+i31−i3−1−i31+i32ζ7−2ζ72ζ11−2ζ11000000000000000000000000
χ624-44-400-24i−4i002-222i3−2i32i3−2i30000−2i2i−23230000-22−2i2i0000001−i3−1+i31+i3−1−i3−2ζ72ζ7−2ζ112ζ11000000000000000000000000
χ634-44-400-2−4i4i002-22−2i32i3−2i32i300002i−2i−232300002-2−2i2i000000−1−i31+i3−1+i31−i3−2ζ112ζ11−2ζ72ζ7000000000000000000000000
χ644-44-400-2−4i4i002-22−2i32i3−2i32i300002i−2i−23230000-222i−2i0000001+i3−1−i31−i3−1+i32ζ11−2ζ112ζ7−2ζ7000000000000000000000000
χ654-44-400-2−4i4i002-222i3−2i32i3−2i300002i−2i23−2300002-2−2i2i000000−1+i31−i3−1−i31+i3−2ζ72ζ7−2ζ112ζ11000000000000000000000000
χ664-44-400-2−4i4i002-222i3−2i32i3−2i300002i−2i23−230000-222i−2i0000001−i3−1+i31+i3−1−i32ζ7−2ζ72ζ11−2ζ11000000000000000000000000
χ674-4-444-440000-4-444-4-44000000000000000000000000000000000000000000002-22-2000000
χ684-4-444-440000-4-444-4-4400000000000000000000000000000000000000000000-22-22000000
χ694-4-44-4440000-4-44-444-4000000000000000000000000000000000000000000002-2-22000000
χ704-4-44-4440000-4-44-444-400000000000000000000000000000000000000000000-222-2000000
χ718-8-888-8-4000044-4-444-4000000000000000000000000000000000000000000000000000000
χ728-8-88-88-4000044-44-4-44000000000000000000000000000000000000000000000000000000

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