Finite Group Databasebeta

← Group #10697302

Character table — Group #10697302

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888888888888888824242424484848484848
order12222234444446661212121244466121212121212121212128888888888882424242424242424242424242424242424242424242424244444244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-11-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111
χ511111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ611111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-11-1-1-1
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1111
χ9222222222-222-2222-2-2-2-2-2-2-22222-2-2-2-222-2-222-2-200000000000000002222-2-2-2-2000000000000000000
χ10222222222-222-2222-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-2220000000000000000-2-2-2-22222000000000000000000
χ112222222-2-22-2-2222222222-2-222-2-222-2-2-2-2-2-2000022-2-200002222-2-2-2-200000000000000000000000000
χ122222222-2-22-2-2222222222-2-222-2-222-2-2-2-2-2-20000-2-2220000-2-2-2-2222200000000000000000000000000
χ132222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-2-222-2-2220000000022-2-200000000000000002222-2-2-2-20000000000
χ142222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-2-222-2-22200000000-2-2220000000000000000-2-2-2-222220000000000
χ15222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ16222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000
χ17222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000
χ18222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000
χ19222222-122-222-2-1-1-11111-2-2-2-1-1-1-11111-1-11122-2-20000000033−3−333−3−3-1-1-1-1111133−3−333−3−30000000000
χ20222222-122-222-2-1-1-11111-2-2-2-1-1-1-11111-1-11122-2-200000000−3−333−3−333-1-1-1-11111−3−333−3−3330000000000
χ21222222-122-222-2-1-1-11111-2-2-2-1-1-1-11111-1-111-2-2220000000033−3−333−3−31111-1-1-1-1−3−333−3−3330000000000
χ22222222-122-222-2-1-1-11111-2-2-2-1-1-1-11111-1-111-2-22200000000−3−333−3−3331111-1-1-1-133−3−333−3−30000000000
χ23222222-1-2-22-2-22-1-1-1-1-1-1-12-2-2-1-111-1-1111111000022-2-20000-1-1-1-1111133−3−333−3−333−3−3−3−3330000000000
χ24222222-1-2-22-2-22-1-1-1-1-1-1-12-2-2-1-111-1-1111111000022-2-20000-1-1-1-11111−3−333−3−333−3−33333−3−30000000000
χ25222222-1-2-22-2-22-1-1-1-1-1-1-12-2-2-1-111-1-11111110000-2-22200001111-1-1-1-133−3−333−3−3−3−33333−3−30000000000
χ26222222-1-2-22-2-22-1-1-1-1-1-1-12-2-2-1-111-1-11111110000-2-22200001111-1-1-1-1−3−333−3−33333−3−3−3−3330000000000
χ27222222-1-2-2-2-2-2-2-1-1-11111-222-1-11111-1-111-1-10000000022-2-233−3−3−3−333−3−33333−3−3-1-1-1-111110000000000
χ28222222-1-2-2-2-2-2-2-1-1-11111-222-1-11111-1-111-1-10000000022-2-2−3−33333−3−333−3−3−3−333-1-1-1-111110000000000
χ29222222-1-2-2-2-2-2-2-1-1-11111-222-1-11111-1-111-1-100000000-2-22233−3−3−3−33333−3−3−3−3331111-1-1-1-10000000000
χ30222222-1-2-2-2-2-2-2-1-1-11111-222-1-11111-1-111-1-100000000-2-222−3−33333−3−3−3−33333−3−31111-1-1-1-10000000000
χ312222-2-22222-2-222222222-2-22-2-222-2-2-2-2-2-2220000000000000000000000000000000000000000020-200
χ322222-2-22222-2-222222222-2-22-2-222-2-2-2-2-2-22200000000000000000000000000000000000000000-20200
χ332222-2-2222-2-2-2-2222-2-2-2-222-2-2-2222222-2-2-2-20000000000000000000000000000000000002i2i−2i−2i000000
χ342222-2-2222-2-2-2-2222-2-2-2-222-2-2-2222222-2-2-2-2000000000000000000000000000000000000−2i−2i2i2i000000
χ352222-2-22-2-222222222222-22-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000000000020-2000
χ362222-2-22-2-222222222222-22-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000000000-202000
χ372222-2-22-2-2-222-2222-2-2-2-22-22-2-2-2-222-2-22222000000000000000000000000000000000000000000002-2
χ382222-2-22-2-2-222-2222-2-2-2-22-22-2-2-2-222-2-2222200000000000000000000000000000000000000000000-22
χ3922-2-2-2222-202-202-2-200000002-22-200002-200002i−2i−i2i2−i2i22−22−2−i2i2−i2i2−i2i2−i2i200002i−2i2i−2i2−22−22−22−20000000000
χ4022-2-2-2222-202-202-2-200000002-22-200002-200002i−2ii2−i2i2−i2−22−22i2−i2i2−i2i2−i2i2−i200002i−2i2i−2i−22−22−22−220000000000
χ4122-2-2-2222-202-202-2-200000002-22-200002-20000−2i2i−i2i2−i2i2−22−22−i2i2−i2i2−i2i2−i2i20000−2i2i−2i2i−22−22−22−220000000000
χ4222-2-2-2222-202-202-2-200000002-22-200002-20000−2i2ii2−i2i2−i22−22−2i2−i2i2−i2i2−i2i2−i20000−2i2i−2i2i2−22−22−22−20000000000
χ4322-2-2-222-220-2202-2-200000002-2-220000-22002i−2i00−i2i2i2−i22−2−22−i2i2−i2i2i2−i2i2−i22i−2i2i−2i00002−22−2−22−220000000000
χ4422-2-2-222-220-2202-2-200000002-2-220000-22002i−2i00i2−i2−i2i2−222−2i2−i2i2−i2−i2i2−i2i22i−2i2i−2i0000−22−222−22−20000000000
χ4522-2-2-222-220-2202-2-200000002-2-220000-2200−2i2i00−i2i2i2−i2−222−2−i2i2−i2i2i2−i2i2−i2−2i2i−2i2i0000−22−222−22−20000000000
χ4622-2-2-222-220-2202-2-200000002-2-220000-2200−2i2i00i2−i2−i2i22−2−22i2−i2i2−i2−i2i2−i2i2−2i2i−2i2i00002−22−2−22−220000000000
χ4722-2-2-22-12-202-20-1113−33−3000-11-113−33−3-113−3002i−2i−i2i2−i2i22−22−2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23i3−i3−i3i3−ii−iiζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ4822-2-2-22-12-202-20-1113−33−3000-11-113−33−3-113−3002i−2ii2−i2i2−i2−22−22−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i3−i3−i3i3−ii−ii−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ4922-2-2-22-12-202-20-1113−33−3000-11-113−33−3-113−300−2i2i−i2i2−i2i2−22−22ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i3i3i3−i3i−ii−i−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ5022-2-2-22-12-202-20-1113−33−3000-11-113−33−3-113−300−2i2ii2−i2i2−i22−22−2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−i3i3i3−i3i−ii−iζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ5122-2-2-22-12-202-20-111−33−33000-11-11−33−33-11−33002i−2i−i2i2−i2i22−22−2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i3i3i3−i3−ii−iiζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ5222-2-2-22-12-202-20-111−33−33000-11-11−33−33-11−33002i−2ii2−i2i2−i2−22−22−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−i3i3i3−i3−ii−ii−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ5322-2-2-22-12-202-20-111−33−33000-11-11−33−33-11−3300−2i2i−i2i2−i2i2−22−22ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7i3−i3−i3i3i−ii−i−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ5422-2-2-22-12-202-20-111−33−33000-11-11−33−33-11−3300−2i2ii2−i2i2−i22−22−2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i3−i3−i3i3i−ii−iζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ5522-2-2-22-1-220-220-1113−33−3000-111-13−3−331-1−332i−2i00−i2i2i2−i22−2−22ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ii−ii−i3i3i3−i3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ5622-2-2-22-1-220-220-1113−33−3000-111-13−3−331-1−332i−2i00i2−i2−i2i2−222−2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ii−ii−i3i3i3−i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ5722-2-2-22-1-220-220-1113−33−3000-111-13−3−331-1−33−2i2i00−i2i2i2−i2−222−2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i−ii−ii3−i3−i3i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ5822-2-2-22-1-220-220-1113−33−3000-111-13−3−331-1−33−2i2i00i2−i2−i2i22−2−22−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23i−ii−ii3−i3−i3i3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ5922-2-2-22-1-220-220-111−33−33000-111-1−333−31-13−32i−2i00−i2i2i2−i22−2−22ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ii−iii3−i3−i3i3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ6022-2-2-22-1-220-220-111−33−33000-111-1−333−31-13−32i−2i00i2−i2−i2i2−222−2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ii−iii3−i3−i3i3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ6122-2-2-22-1-220-220-111−33−33000-111-1−333−31-13−3−2i2i00−i2i2i2−i2−222−2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i−ii−i−i3i3i3−i3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ6222-2-2-22-1-220-220-111−33−33000-111-1−333−31-13−3−2i2i00i2−i2−i2i22−2−22−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7i−ii−i−i3i3i3−i3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ634444-4-4-2444-4-44-2-2-2-2-2-2-2-4-4422-2-2222222-2-20000000000000000000000000000000000000000000000
χ644444-4-4-244-4-4-4-4-2-2-2222244-422-2-2-2-2-2-222220000000000000000000000000000000000000000000000
χ654444-4-4-2-4-44444-2-2-2-2-2-2-2-44-4222222-2-2-2-2220000000000000000000000000000000000000000000000
χ664444-4-4-2-4-4-444-4-2-2-222224-442222-2-222-2-2-2-20000000000000000000000000000000000000000000000
χ6744-4-44-444-40-4404-4-40000000-444-40000-44000000000000000000000000000000000000000000000000
χ6844-4-44-44-4404-404-4-40000000-44-4400004-4000000000000000000000000000000000000000000000000
χ6944-4-44-4-24-40-440-22223−2323−230002-2-22−2323−23232-223−230000000000000000000000000000000000000000000000
χ7044-4-44-4-24-40-440-222−2323−23230002-2-2223−2323−232-2−23230000000000000000000000000000000000000000000000
χ7144-4-44-4-2-4404-40-22223−2323−230002-22-2−232323−23-22−23230000000000000000000000000000000000000000000000
χ7244-4-44-4-2-4404-40-222−2323−23230002-22-223−23−2323-2223−230000000000000000000000000000000000000000000000
χ734-44-400400400-4-44-444-4-40000000000000000000000000000000000000000000000000002-22-2000000
χ744-44-400400400-4-44-444-4-4000000000000000000000000000000000000000000000000000-22-22000000
χ754-44-400400-4004-44-4-4-4440000000000000000000000000000000000000000000000000002i−2i−2i2i000000
χ764-44-400400-4004-44-4-4-444000000000000000000000000000000000000000000000000000−2i2i2i−2i000000
χ778-88-800-400800-84-44-4-4440000000000000000000000000000000000000000000000000000000000000
χ788-88-800-400-80084-4444-4-40000000000000000000000000000000000000000000000000000000000000
χ798-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ808-8-8800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000
χ818-8-8800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.