Finite Group Databasebeta

← Group #10695873

Character table — Group #10695873

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order1222222234466624446666661212121244441212121212121212121288882424242424242424888888882444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222-2-22222-2-2-2222222-2-2-2-20000-2-200000000002i−2i00002i2i−2i−2i000000000000
χ10222222222-2-22222-2-2-2222222-2-2-2-20000-2-20000000000−2i2i0000−2i−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
χ1322222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-11111000000000000
χ1422222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-1000000000000
χ1522222222-1-2-2-1-1-12-2-2-2-1-1-1-1-1-11111000011−i3−i3−i3−i3i3i3i3i3002i−2i33−3−3−i−iii000000000000
χ1622222222-1-2-2-1-1-12-2-2-2-1-1-1-1-1-11111000011−i3−i3−i3−i3i3i3i3i300−2i2i−3−333ii−i−i000000000000
χ1722222222-1-2-2-1-1-12-2-2-2-1-1-1-1-1-11111000011i3i3i3i3−i3−i3−i3−i3002i−2i−3−333−i−iii000000000000
χ1822222222-1-2-2-1-1-12-2-2-2-1-1-1-1-1-11111000011i3i3i3i3−i3−i3−i3−i300−2i2i33−3−3ii−i−i000000000000
χ19222222-2-2222222-2-22-222-2-2-2-222-2-200002-200000000000000000000000000002-200
χ20222222-2-2222222-2-22-222-2-2-2-222-2-200002-20000000000000000000000000000-2200
χ21222222-2-22-2-2222-22-2222-2-2-2-2-2-2220000-2200000000000000000000000022-2-20000
χ22222222-2-22-2-2222-22-2222-2-2-2-2-2-2220000-22000000000000000000000000-2-2220000
χ232222-2-222222222-2-2-22-2-222-2-222-2-20000-220000000000000000000000000000002-2
χ242222-2-222222222-2-2-22-2-222-2-222-2-20000-22000000000000000000000000000000-22
χ252222-2-2222-2-2222-222-2-2-222-2-2-2-22200002-20000000000000000000022-2-200000000
χ262222-2-2222-2-2222-222-2-2-222-2-2-2-22200002-200000000000000000000-2-22200000000
χ272222-2-2-2-222222222-2-2-2-2-2-22222220000-2-2000000002-2002-22-20000000000000000
χ282222-2-2-2-222222222-2-2-2-2-2-22222220000-2-200000000-2200-22-220000000000000000
χ292222-2-2-2-22-2-22222-222-2-2-2-222-2-2-2-222-2-22222-2-222-2-2000000000000000000000000
χ302222-2-2-2-22-2-22222-222-2-2-2-222-2-2-2-2-2-22222-2-222-2-222000000000000000000000000
χ312222-2-2-2-2-122-1-1-122-2-21111-1-1-1-1-1-1000011−i3−i3i3i3i3i3−i3−i32-200-11-11−i3i3−i3i3000000000000
χ322222-2-2-2-2-122-1-1-122-2-21111-1-1-1-1-1-1000011−i3−i3i3i3i3i3−i3−i3-22001-11-1i3−i3i3−i3000000000000
χ332222-2-2-2-2-122-1-1-122-2-21111-1-1-1-1-1-1000011i3i3−i3−i3−i3−i3i3i32-200-11-11i3−i3i3−i3000000000000
χ342222-2-2-2-2-122-1-1-122-2-21111-1-1-1-1-1-1000011i3i3−i3−i3−i3−i3i3i3-22001-11-1−i3i3−i3i3000000000000
χ352222-2-2-2-2-1-2-2-1-1-12-2221111-1-1111122-2-2-1-1-1-111-1-11100003−3−333−3−33000000000000
χ362222-2-2-2-2-1-2-2-1-1-12-2221111-1-1111122-2-2-1-1-1-111-1-1110000−333−3−333−3000000000000
χ372222-2-2-2-2-1-2-2-1-1-12-2221111-1-11111-2-222-1-111-1-111-1-100003−3−33−333−3000000000000
χ382222-2-2-2-2-1-2-2-1-1-12-2221111-1-11111-2-222-1-111-1-111-1-10000−333−33−3−33000000000000
χ39444444-4-4-244-2-2-2-4-44-4-2-22222-2-2220000-2200000000000000000000000000000000
χ40444444-4-4-2-4-4-2-2-2-44-44-2-2222222-2-200002-200000000000000000000000000000000
χ414444-4-444-244-2-2-2-4-4-4422-2-222-2-22200002-200000000000000000000000000000000
χ424444-4-444-2-4-4-2-2-2-444-422-2-22222-2-20000-2200000000000000000000000000000000
χ4344-4-44-4004004-4-400004-4000000000000000000000000000000000000000022−220000
χ4444-4-44-4004004-4-400004-40000000000000000000000000000000000000000−22220000
χ4544-4-4-44004004-4-40000-440000000000000000000000000000000000000022−22000000
χ4644-4-4-44004004-4-40000-4400000000000000000000000000000000000000−2222000000
χ474-44-4000044-4-4-4400000000004-4002-22-2002-22-22-22-2000000000000000000000000
χ484-44-4000044-4-4-4400000000004-400-22-2200-22-22-22-22000000000000000000000000
χ494-44-400004-44-4-440000000000-44002-2-22002-2-222-2-22000000000000000000000000
χ504-44-400004-44-4-440000000000-4400-222-200-222-2-222-2000000000000000000000000
χ514-44-40000-24-422-200000000−2i32i3-22−2i32i32-22-200−1−i31+i3−1+i31−i3−1+i31−i3−1−i31+i3000000000000000000000000
χ524-44-40000-24-422-200000000−2i32i3-22−2i32i3-22-22001+i3−1−i31−i3−1+i31−i3−1+i31+i3−1−i3000000000000000000000000
χ534-44-40000-24-422-2000000002i3−2i3-222i3−2i32-22-200−1+i31−i3−1−i31+i3−1−i31+i3−1+i31−i3000000000000000000000000
χ544-44-40000-24-422-2000000002i3−2i3-222i3−2i3-22-22001−i3−1+i31+i3−1−i31+i3−1−i31−i3−1+i3000000000000000000000000
χ554-44-40000-2-4422-200000000−2i32i32-22i3−2i32-2-2200−1−i31+i31−i3−1+i3−1+i31−i31+i3−1−i3000000000000000000000000
χ564-44-40000-2-4422-200000000−2i32i32-22i3−2i3-222-2001+i3−1−i3−1+i31−i31−i3−1+i3−1−i31+i3000000000000000000000000
χ574-44-40000-2-4422-2000000002i3−2i32-2−2i32i32-2-2200−1+i31−i31+i3−1−i3−1−i31+i31−i3−1+i3000000000000000000000000
χ584-44-40000-2-4422-2000000002i3−2i32-2−2i32i3-222-2001−i3−1+i3−1−i31+i31+i3−1−i3−1+i31−i3000000000000000000000000
χ594-4-44004-4400-44-40000004-40000000000000000000000000000000000−2i22i200000000
χ604-4-44004-4400-44-40000004-400000000000000000000000000000000002i2−2i200000000
χ614-4-4400-44400-44-4000000-4400000000000000000000000000000000−2i22i20000000000
χ624-4-4400-44400-44-4000000-44000000000000000000000000000000002i2−2i20000000000
χ6388-8-88-800-400-4440000-440000000000000000000000000000000000000000000000
χ6488-8-8-8800-400-44400004-40000000000000000000000000000000000000000000000
χ658-8-88008-8-4004-44000000-4400000000000000000000000000000000000000000000
χ668-8-8800-88-4004-440000004-400000000000000000000000000000000000000000000

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