Finite Group Databasebeta

← Group #10695879

Character table — Group #10695879

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order12222222344666244466666612121212222266666666121288882424242424242424888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-11-11
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-11-1
χ9222222222-2-22222-2-2-2222222-2-2-2-2000000000000-2-2002i−2i00002i2i−2i−2i000000000000
χ10222222222-2-22222-2-2-2222222-2-2-2-2000000000000-2-200−2i2i0000−2i−2i2i2i000000000000
χ1122222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ1222222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ1322222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111-1-122-2-2-1-1-1-11111000000000000
χ1422222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111-1-1-2-2221111-1-1-1-1000000000000
χ1522222222-1-2-2-1-1-12-2-2-2-1-1-1-1-1-111110000−i3−i3−i3−i3i3i3i3i311002i−2i33−3−3−i−iii000000000000
χ1622222222-1-2-2-1-1-12-2-2-2-1-1-1-1-1-111110000−i3−i3−i3−i3i3i3i3i31100−2i2i−3−333ii−i−i000000000000
χ1722222222-1-2-2-1-1-12-2-2-2-1-1-1-1-1-111110000i3i3i3i3−i3−i3−i3−i311002i−2i−3−333−i−iii000000000000
χ1822222222-1-2-2-1-1-12-2-2-2-1-1-1-1-1-111110000i3i3i3i3−i3−i3−i3−i31100−2i2i33−3−3ii−i−i000000000000
χ19222222-2-2222222-2-22-222-2-2-2-222-2-20000000000002-20000000000000000000020-20
χ20222222-2-2222222-2-22-222-2-2-2-222-2-20000000000002-200000000000000000000-2020
χ21222222-2-22-2-2222-22-2222-2-2-2-2-2-222000000000000-22000000000000000022-2-20000
χ22222222-2-22-2-2222-22-2222-2-2-2-2-2-222000000000000-220000000000000000-2-2220000
χ232222-2-222222222-2-2-22-2-222-2-222-2-2000000000000-2200000000000000000000020-2
χ242222-2-222222222-2-2-22-2-222-2-222-2-2000000000000-22000000000000000000000-202
χ252222-2-2222-2-2222-222-2-2-222-2-2-2-2220000000000002-200000000000022-2-200000000
χ262222-2-2222-2-2222-222-2-2-222-2-2-2-2220000000000002-2000000000000-2-22200000000
χ272222-2-2-2-222222222-2-2-2-2-2-2222222000000000000-2-22-2002-22-20000000000000000
χ282222-2-2-2-222222222-2-2-2-2-2-2222222000000000000-2-2-2200-22-220000000000000000
χ292222-2-2-2-22-2-22222-222-2-2-2-222-2-2-2-222-2-222-2-222-2-222000000000000000000000000
χ302222-2-2-2-22-2-22222-222-2-2-2-222-2-2-2-2-2-222-2-222-2-22222000000000000000000000000
χ312222-2-2-2-2-122-1-1-122-2-21111-1-1-1-1-1-10000−i3−i3i3i3i3i3−i3−i3112-200-11-11−i3i3−i3i3000000000000
χ322222-2-2-2-2-122-1-1-122-2-21111-1-1-1-1-1-10000−i3−i3i3i3i3i3−i3−i311-22001-11-1i3−i3i3−i3000000000000
χ332222-2-2-2-2-122-1-1-122-2-21111-1-1-1-1-1-10000i3i3−i3−i3−i3−i3i3i3112-200-11-11i3−i3i3−i3000000000000
χ342222-2-2-2-2-122-1-1-122-2-21111-1-1-1-1-1-10000i3i3−i3−i3−i3−i3i3i311-22001-11-1−i3i3−i3i3000000000000
χ352222-2-2-2-2-1-2-2-1-1-12-2221111-1-1111122-2-2-1-111-1-111-1-100003−3−333−3−33000000000000
χ362222-2-2-2-2-1-2-2-1-1-12-2221111-1-1111122-2-2-1-111-1-111-1-10000−333−3−333−3000000000000
χ372222-2-2-2-2-1-2-2-1-1-12-2221111-1-11111-2-22211-1-111-1-1-1-100003−3−33−333−3000000000000
χ382222-2-2-2-2-1-2-2-1-1-12-2221111-1-11111-2-22211-1-111-1-1-1-10000−333−33−3−33000000000000
χ39444444-4-4-244-2-2-2-4-44-4-2-22222-2-222000000000000-22000000000000000000000000
χ40444444-4-4-2-4-4-2-2-2-44-44-2-2222222-2-20000000000002-2000000000000000000000000
χ414444-4-444-244-2-2-2-4-4-4422-2-222-2-2220000000000002-2000000000000000000000000
χ424444-4-444-2-4-4-2-2-2-444-422-2-22222-2-2000000000000-22000000000000000000000000
χ4344-4-4004-44004-4-40000004-40000000000000000000000000000000000−2i22i200000000
χ4444-4-4004-44004-4-40000004-400000000000000000000000000000000002i2−2i200000000
χ4544-4-400-444004-4-4000000-4400000000000000000000000000000000−2i22i20000000000
χ4644-4-400-444004-4-4000000-44000000000000000000000000000000002i2−2i20000000000
χ474-44-44-400400-44-400004-40000000000000000000000000000000000000000−2i22i20000
χ484-44-44-400400-44-400004-400000000000000000000000000000000000000002i2−2i20000
χ494-44-4-4400400-44-40000-4400000000000000000000000000000000000000−2i22i2000000
χ504-44-4-4400400-44-40000-44000000000000000000000000000000000000002i2−2i2000000
χ514-4-44000044-4-4-4400000000004-4002-22-22-22-22-22-200000000000000000000000000
χ524-4-44000044-4-4-4400000000004-400-22-22-22-22-22-2200000000000000000000000000
χ534-4-4400004-44-4-440000000000-44002-2-222-2-222-2-2200000000000000000000000000
χ544-4-4400004-44-4-440000000000-4400-222-2-222-2-222-200000000000000000000000000
χ554-4-440000-24-422-200000000−2i32i3-22−2i32i32-22-2−1−i31+i3−1+i31−i3−1+i31−i3−1−i31+i300000000000000000000000000
χ564-4-440000-24-422-200000000−2i32i3-22−2i32i3-22-221+i3−1−i31−i3−1+i31−i3−1+i31+i3−1−i300000000000000000000000000
χ574-4-440000-24-422-2000000002i3−2i3-222i3−2i32-22-2−1+i31−i3−1−i31+i3−1−i31+i3−1+i31−i300000000000000000000000000
χ584-4-440000-24-422-2000000002i3−2i3-222i3−2i3-22-221−i3−1+i31+i3−1−i31+i3−1−i31−i3−1+i300000000000000000000000000
χ594-4-440000-2-4422-200000000−2i32i32-22i3−2i32-2-22−1−i31+i31−i3−1+i3−1+i31−i31+i3−1−i300000000000000000000000000
χ604-4-440000-2-4422-200000000−2i32i32-22i3−2i3-222-21+i3−1−i3−1+i31−i31−i3−1+i3−1−i31+i300000000000000000000000000
χ614-4-440000-2-4422-2000000002i3−2i32-2−2i32i32-2-22−1+i31−i31+i3−1−i3−1−i31+i31−i3−1+i300000000000000000000000000
χ624-4-440000-2-4422-2000000002i3−2i32-2−2i32i3-222-21−i3−1+i3−1−i31+i31+i3−1−i3−1+i31−i300000000000000000000000000
χ6388-8-8008-8-400-444000000-4400000000000000000000000000000000000000000000
χ6488-8-800-88-400-4440000004-400000000000000000000000000000000000000000000
χ658-88-88-800-4004-440000-440000000000000000000000000000000000000000000000
χ668-88-8-8800-4004-4400004-40000000000000000000000000000000000000000000000

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