Finite Group Databasebeta

← Group #10695926

Character table — Group #10695926

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888888888888888824242424484848484848
order12222234444446661212121244466121212121212121212124444888888881212121212121212242424242424242424242424242424242244244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ511111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ611111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ92222222222-2-22222-2-2-2-2-2-2-222-2-22222-2-2-2-222-2-2000000002222-2-2-2-200000000000000000000000000
χ102222222222-2-22222-2-2-2-2-2-2-222-2-22222-2-2-2-2-2-22200000000-2-2-2-2222200000000000000000000000000
χ112222222-2-2-222-222222222-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000002-200
χ122222222-2-2-222-222222222-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000-2200
χ132222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-2-2-2-2222200000000000000000000000000000000000022-2-2000000
χ142222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-2-2-2-22222000000000000000000000000000000000000-2-222000000
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
χ16222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000
χ17222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000
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
χ19222222-1222-2-22-1-1-11111-2-2-2-1-111-1-1-1-1111122-2-200000000-1-1-1-111113333−3−3−3−33333−3−3−3−30000000000
χ20222222-1222-2-22-1-1-11111-2-2-2-1-111-1-1-1-1111122-2-200000000-1-1-1-11111−3−3−3−33333−3−3−3−333330000000000
χ21222222-1222-2-22-1-1-11111-2-2-2-1-111-1-1-1-11111-2-222000000001111-1-1-1-13333−3−3−3−3−3−3−3−333330000000000
χ22222222-1222-2-22-1-1-11111-2-2-2-1-111-1-1-1-11111-2-222000000001111-1-1-1-1−3−3−3−333333333−3−3−3−30000000000
χ232222-2-2222-222-22222222-2-22-2-2-2-222-2-2-2-2220000000022-2-2000000000000000022-2-222-2-20000000000
χ242222-2-2222-222-22222222-2-22-2-2-2-222-2-2-2-22200000000-2-2220000000000000000-2-222-2-2220000000000
χ252222-2-2222-2-2-2-2222-2-2-2-222-2-2-22222-2-222-2-200002i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ262222-2-2222-2-2-2-2222-2-2-2-222-2-2-22222-2-222-2-20000−2i−2i2i2i000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ272222-2-22-2-222222222222-22-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000000000000002-2
χ282222-2-22-2-222222222222-22-2-2-2-2-2-2-22222-2-200000000000000000000000000000000000000000000-22
χ292222-2-22-2-22-2-22222-2-2-2-22-22-2-222-2-222-2-22200000000000000000000000000000000000000002-20000
χ302222-2-22-2-22-2-22222-2-2-2-22-22-2-222-2-222-2-2220000000000000000000000000000000000000000-220000
χ312222-2-2-122-222-2-1-1-1-1-1-1-1-2-221111-1-11111-1-10000000022-2-2−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3-1-111-1-1110000000000
χ322222-2-2-122-222-2-1-1-1-1-1-1-1-2-221111-1-11111-1-10000000022-2-2i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3-1-111-1-1110000000000
χ332222-2-2-122-222-2-1-1-1-1-1-1-1-2-221111-1-11111-1-100000000-2-222−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i311-1-111-1-10000000000
χ342222-2-2-122-222-2-1-1-1-1-1-1-1-2-221111-1-11111-1-100000000-2-222i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i311-1-111-1-10000000000
χ352222-2-2-122-2-2-2-2-1-1-1111122-211-1-1-1-111-1-11100002i2i−2i−2i0000−i3−i3i3i3i3i3−i3−i3−i−iii−i−iii33−3−3−3−3330000000000
χ362222-2-2-122-2-2-2-2-1-1-1111122-211-1-1-1-111-1-11100002i2i−2i−2i0000i3i3−i3−i3−i3−i3i3i3−i−iii−i−iii−3−33333−3−30000000000
χ372222-2-2-122-2-2-2-2-1-1-1111122-211-1-1-1-111-1-1110000−2i−2i2i2i0000−i3−i3i3i3i3i3−i3−i3ii−i−iii−i−i−3−33333−3−30000000000
χ382222-2-2-122-2-2-2-2-1-1-1111122-211-1-1-1-111-1-1110000−2i−2i2i2i0000i3i3−i3−i3−i3−i3i3i3ii−i−iii−i−i33−3−3−3−3330000000000
χ392-2-222-222-2200-2-22-200000002-2002-22-200002i−2i00−i2i2−i2i22−22−22i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000
χ402-2-222-222-2200-2-22-200000002-2002-22-200002i−2i00i2−i2i2−i2−22−222i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000
χ412-2-222-222-2200-2-22-200000002-2002-22-20000−2i2i00−i2i2−i2i2−22−22−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000
χ422-2-222-222-2200-2-22-200000002-2002-22-20000−2i2i00i2−i2i2−i22−22−2−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i22−22−22−22−20000000000
χ432-2-222-2-12-2200-21-1133−3−3000-113−3-11-113−33−32i−2i00−i2i2−i2i22−22−2−ii−ii−i3i3−i3i3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ70000000000
χ442-2-222-2-12-2200-21-1133−3−3000-113−3-11-113−33−32i−2i00i2−i2i2−i2−22−22−ii−ii−i3i3−i3i3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ70000000000
χ452-2-222-2-12-2200-21-1133−3−3000-113−3-11-113−33−3−2i2i00−i2i2−i2i2−22−22i−ii−ii3−i3i3−i3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ70000000000
χ462-2-222-2-12-2200-21-1133−3−3000-113−3-11-113−33−3−2i2i00i2−i2i2−i22−22−2i−ii−ii3−i3i3−i3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ70000000000
χ472-2-222-2-12-2200-21-11−3−333000-11−33-11-11−33−332i−2i00−i2i2−i2i22−22−2−ii−iii3−i3i3−i3ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ230000000000
χ482-2-222-2-12-2200-21-11−3−333000-11−33-11-11−33−332i−2i00i2−i2i2−i2−22−22−ii−iii3−i3i3−i3−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ230000000000
χ492-2-222-2-12-2200-21-11−3−333000-11−33-11-11−33−33−2i2i00−i2i2−i2i2−22−22i−ii−i−i3i3−i3i3ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ230000000000
χ502-2-222-2-12-2200-21-11−3−333000-11−33-11-11−33−33−2i2i00i2−i2i2−i22−22−2i−ii−i−i3i3−i3i3−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ230000000000
χ512-2-22-2222-2-2002-22-20000000-22002-2-220000002-22−2−222−2−220000-222-22−2−222−2−222−2−222−2−220000000000
χ522-2-22-2222-2-2002-22-20000000-22002-2-220000002-2−222−2−222−20000-222-2−222−2−222−2−222−2−222−20000000000
χ532-2-22-2222-2-2002-22-20000000-22002-2-22000000-222−2−22−222−200002-2-222−2−222−2−22−222−2−222−20000000000
χ542-2-22-2222-2-2002-22-20000000-22002-2-22000000-22−222−22−2−2200002-2-22−222−2−222−22−2−222−2−220000000000
χ552-2-22-22-12-2-20021-1133−3−30001-1−33-111-1−333−3002-22−2−222−2−22−333−31-1-11ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ70000000000
χ562-2-22-22-12-2-20021-1133−3−30001-1−33-111-1−333−3002-2−222−2−222−2−333−31-1-11−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ70000000000
χ572-2-22-22-12-2-20021-1133−3−30001-1−33-111-1−333−300-222−2−22−222−23−3−33-111-1ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ70000000000
χ582-2-22-22-12-2-20021-1133−3−30001-1−33-111-1−333−300-22−222−22−2−223−3−33-111-1−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ70000000000
χ592-2-22-22-12-2-20021-11−3−3330001-13−3-111-13−3−33002-22−2−222−2−223−3−331-1-11ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ230000000000
χ602-2-22-22-12-2-20021-11−3−3330001-13−3-111-13−3−33002-2−222−2−222−23−3−331-1-11−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ230000000000
χ612-2-22-22-12-2-20021-11−3−3330001-13−3-111-13−3−3300-222−2−22−222−2−333−3-111-1ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ230000000000
χ622-2-22-22-12-2-20021-11−3−3330001-13−3-111-13−3−3300-22−222−22−2−22−333−3-111-1−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ230000000000
χ63444444-2-4-4-444-4-2-2-2-2-2-2-24-4-4-2-2-2-2222222220000000000000000000000000000000000000000000000
χ64444444-2-4-4-4-4-4-4-2-2-22222-444-2-2222222-2-2-2-20000000000000000000000000000000000000000000000
χ654444-4-4-2-4-44444-2-2-2-2-2-2-2-44-4222222-2-2-2-2220000000000000000000000000000000000000000000000
χ664444-4-4-2-4-44-4-44-2-2-222224-4422-2-222-2-222-2-20000000000000000000000000000000000000000000000
χ674-44-40040004i−4i0-4-444i−4i4i−4i0000000000000000000000000000000000000000000000000002-22i−2i000000
χ684-44-40040004i−4i0-4-444i−4i4i−4i000000000000000000000000000000000000000000000000000-22−2i2i000000
χ694-44-4004000−4i4i0-4-44−4i4i−4i4i0000000000000000000000000000000000000000000000000002-2−2i2i000000
χ704-44-4004000−4i4i0-4-44−4i4i−4i4i000000000000000000000000000000000000000000000000000-222i−2i000000
χ714-4-444-44-44-4004-44-400000004-400-44-4400000000000000000000000000000000000000000000000000
χ724-4-444-4-2-44-40042-222323−23−23000-2223−232-22-2−2323−23230000000000000000000000000000000000000000000000
χ734-4-444-4-2-44-40042-22−23−232323000-22−23232-22-223−2323−230000000000000000000000000000000000000000000000
χ744-4-44-444-44400-4-44-40000000-4400-444-400000000000000000000000000000000000000000000000000
χ754-4-44-44-2-44400-42-222323−23−230002-2−23232-2-2223−23−23230000000000000000000000000000000000000000000000
χ764-4-44-44-2-44400-42-22−23−2323230002-223−232-2-22−232323−230000000000000000000000000000000000000000000000
χ7788-8-80080000008-8-800000000000000000000000000000000000000000000000000000000000000000
χ7888-8-800-4000000-444−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000000000
χ7988-8-800-4000000-4444i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000000000
χ808-88-800-40008i−8i044-4−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000
χ818-88-800-4000−8i8i044-44i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000

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