Finite Group Databasebeta

← Group #10696531

Character table — Group #10696531

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222224444444444444448888888888888816161616161616161616161624242424484848484848
order122222344666444446612121212121212128888121224242424242424242466881212242424244444222488
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ5111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-1
χ8111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111
χ9222222222222-22-2-2-222-2-222-2-2-2-20000-22000000002-22200-2-200000000000000
χ10222222222222-22-2-2-222-2-222-2-2-2-20000-2200000000-22-2-2002200000000000000
χ112222222-2-22222-2-22-22222-2-222-2-20000-2-20000000000000000000022-2-2000000
χ122222222-2-22222-2-22-22222-2-222-2-20000-2-200000000000000000000-2-222000000
χ132222222-2-2222-2-22-2222-2-2-2-2-2-22200002-20000000000000000000000002-20000
χ142222222-2-2222-2-22-2222-2-2-2-2-2-22200002-2000000000000000000000000-220000
χ15222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-10000000000
χ16222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-211-2-21111110000000000
χ17222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-1-1-2-2-1-111110000000000
χ18222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2112211-1-1-1-10000000000
χ19222222-122-1-1-1-22-2-2-2-1-111-1-1111100001-13333−3−3−3−32-2-1-1001133−3−30000000000
χ20222222-122-1-1-1-22-2-2-2-1-111-1-1111100001-13333−3−3−3−3-221100-1-1−3−3330000000000
χ21222222-122-1-1-1-22-2-2-2-1-111-1-1111100001-1−3−3−3−333332-2-1-10011−3−3330000000000
χ22222222-122-1-1-1-22-2-2-2-1-111-1-1111100001-1−3−3−3−33333-221100-1-133−3−30000000000
χ232222-2-22222222-2-2-22-2-22222-2-2220000-2-2000000000000000000000000002-200
χ242222-2-22222222-2-2-22-2-22222-2-2220000-2-200000000000000000000000000-2200
χ252222-2-2222222-2-222-2-2-2-2-22222-2-200002-200000000000000000000000000002-2
χ262222-2-2222222-2-222-2-2-2-2-22222-2-200002-20000000000000000000000000000-22
χ272222-2-22-2-2222222-2-2-2-222-2-2-2-2-2-20000220000000000002i−2i002i−2i2i−2i0000000000
χ282222-2-22-2-2222222-2-2-2-222-2-2-2-2-2-2000022000000000000−2i2i00−2i2i−2i2i0000000000
χ292222-2-22-2-2222-22-222-2-2-2-2-2-2222222-2-2-2222-2-222-2-20000000000000000000000
χ302222-2-22-2-2222-22-222-2-2-2-2-2-22222-2-222-22-2-222-2-2220000000000000000000000
χ312222-2-2-1-2-2-1-1-1222-2-211-1-11111110000-1-133−3−3−3−33300−i3i32i−2i−i3i3−ii−ii0000000000
χ322222-2-2-1-2-2-1-1-1222-2-211-1-11111110000-1-133−3−3−3−33300i3−i3−2i2ii3−i3i−ii−i0000000000
χ332222-2-2-1-2-2-1-1-1222-2-211-1-11111110000-1-1−3−33333−3−300−i3i3−2i2i−i3i3i−ii−i0000000000
χ342222-2-2-1-2-2-1-1-1222-2-211-1-11111110000-1-1−3−33333−3−300i3−i32i−2ii3−i3−ii−ii0000000000
χ352222-2-2-1-2-2-1-1-1-22-222111111-1-1-1-122-2-21-1-1-111-1-11100−i3i300i3−i3−i3i3i3−i30000000000
χ362222-2-2-1-2-2-1-1-1-22-222111111-1-1-1-122-2-21-1-1-111-1-11100i3−i300−i3i3i3−i3−i3i30000000000
χ372222-2-2-1-2-2-1-1-1-22-222111111-1-1-1-1-2-2221-111-1-111-1-100−i3i300i3−i3i3−i3−i3i30000000000
χ382222-2-2-1-2-2-1-1-1-22-222111111-1-1-1-1-2-2221-111-1-111-1-100i3−i300−i3i3−i3i3i3−i30000000000
χ39444444-2-4-4-2-2-24-4-44-4-2-2-2-222-2-222000022000000000000000000000000000000
χ40444444-2-4-4-2-2-2-4-44-44-2-2222222-2-20000-22000000000000000000000000000000
χ414444-4-4-244-2-2-24-4-4-4422-2-2-2-222-2-2000022000000000000000000000000000000
χ424444-4-4-244-2-2-2-4-444-42222-2-2-2-2220000-22000000000000000000000000000000
χ434-44-40044-4-4-440000000004-40000000000000000000000000000002-22-2000000
χ444-44-40044-4-4-440000000004-4000000000000000000000000000000-22-22000000
χ454-44-4004-44-4-44000000000-440000000000000000000000000000002-2-22000000
χ464-44-4004-44-4-44000000000-44000000000000000000000000000000-222-2000000
χ474-4-444-44004-4-4000004-4000000002-22-2002-22-22-22-20000000000000000000000
χ484-4-444-44004-4-4000004-400000000-22-2200-22-22-22-220000000000000000000000
χ494-4-444-4-200-22200000-2223−230023−23002-22-200−1+31−3−1+31−3−1−31+3−1−31+30000000000000000000000
χ504-4-444-4-200-22200000-2223−230023−2300-22-22001−3−1+31−3−1+31+3−1−31+3−1−30000000000000000000000
χ514-4-444-4-200-22200000-22−232300−2323002-22-200−1−31+3−1−31+3−1+31−3−1+31−30000000000000000000000
χ524-4-444-4-200-22200000-22−232300−232300-22-22001+3−1−31+3−1−31−3−1+31−3−1+30000000000000000000000
χ534-4-44-444004-4-400000-44000000002-2-22002-2-222-2-220000000000000000000000
χ544-4-44-444004-4-400000-4400000000-222-200-222-2-222-20000000000000000000000
χ554-4-44-44-200-222000002-223−2300−2323002-2-2200−1−31+31+3−1−3−1+31−31−3−1+30000000000000000000000
χ564-4-44-44-200-222000002-223−2300−232300-222-2001+3−1−3−1−31+31−3−1+3−1+31−30000000000000000000000
χ574-4-44-44-200-222000002-2−23230023−23002-2-2200−1+31−31−3−1+3−1−31+31+3−1−30000000000000000000000
χ584-4-44-44-200-222000002-2−23230023−2300-222-2001−3−1+3−1+31−31+3−1−3−1−31+30000000000000000000000
χ5988-8-800800-88-8000000000000000000000000000000000000000000000000000
χ6088-8-800-4004-44000000000000043−43000000000000000000000000000000000000
χ6188-8-800-4004-440000000000000−4343000000000000000000000000000000000000
χ628-88-800-48-844-4000000000-440000000000000000000000000000000000000000
χ638-88-800-4-8844-40000000004-40000000000000000000000000000000000000000

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