Finite Group Databasebeta

← Group #10698775

Character table — Group #10698775

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888888888888888824242424484848484848
order12222234444446661212121244466121212121212121212124444888888881212121212121212242424242424242424242424242424248888228888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1
χ611111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ922222222-2-2222222-2-2-2-2-2-2-222-2-22222-2-2-2-222-2-2000000002222-2-2-2-200000000000000000000000000
χ1022222222-2-2222222-2-2-2-2-2-2-222-2-22222-2-2-2-2-2-22200000000-2-2-2-2222200000000000000000000000000
χ112222222-222-2-2-222222222-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000002i−2i00
χ122222222-222-2-2-222222222-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000−2i2i00
χ132222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-2-2-2-22222000000000000000000000000000000000000000000002i−2i
χ142222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-2-2-2-2222200000000000000000000000000000000000000000000−2i2i
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
χ19222222-12-2-2222-1-1-11111-2-2-2-1-111-1-1-1-1111122-2-200000000-1-1-1-111113333−3−3−3−33333−3−3−3−30000000000
χ20222222-12-2-2222-1-1-11111-2-2-2-1-111-1-1-1-1111122-2-200000000-1-1-1-11111−3−3−3−33333−3−3−3−333330000000000
χ21222222-12-2-2222-1-1-11111-2-2-2-1-111-1-1-1-11111-2-222000000001111-1-1-1-13333−3−3−3−3−3−3−3−333330000000000
χ22222222-12-2-2222-1-1-11111-2-2-2-1-111-1-1-1-11111-2-222000000001111-1-1-1-1−3−3−3−333333333−3−3−3−30000000000
χ232222-2-222222-2-22222222-2-22-2-2-2-222-2-2-2-222000022-2-200000000000022-2-222-2-2000000000000000000
χ242222-2-222222-2-22222222-2-22-2-2-2-222-2-2-2-2220000-2-222000000000000-2-222-2-222000000000000000000
χ252222-2-222-2-22-2-2222-2-2-2-222-2-2-22222-2-222-2-2000000002i2i−2i−2i00000000000000002i2i−2i−2i2i2i−2i−2i0000000000
χ262222-2-222-2-22-2-2222-2-2-2-222-2-2-22222-2-222-2-200000000−2i−2i2i2i0000000000000000−2i−2i2i2i−2i−2i2i2i0000000000
χ272222-2-22-222-2222222222-22-2-2-2-2-2-2-22222-2-200000000000000000000000000000000000022-2-2000000
χ282222-2-22-222-2222222222-22-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000000-2-222000000
χ292222-2-22-2-2-2-222222-2-2-2-22-22-2-222-2-222-2-22200000000000000000000000000000000000000002-20000
χ302222-2-22-2-2-2-222222-2-2-2-22-22-2-222-2-222-2-2220000000000000000000000000000000000000000-220000
χ312222-2-2-12222-2-2-1-1-1-1-1-1-1-2-221111-1-11111-1-1000022-2-20000−i3−i3i3i3−i3−i3i3i3-1-111-1-111−i3−i3i3i3i3i3−i3−i30000000000
χ322222-2-2-12222-2-2-1-1-1-1-1-1-1-2-221111-1-11111-1-1000022-2-20000i3i3−i3−i3i3i3−i3−i3-1-111-1-111i3i3−i3−i3−i3−i3i3i30000000000
χ332222-2-2-12222-2-2-1-1-1-1-1-1-1-2-221111-1-11111-1-10000-2-2220000−i3−i3i3i3−i3−i3i3i311-1-111-1-1i3i3−i3−i3−i3−i3i3i30000000000
χ342222-2-2-12222-2-2-1-1-1-1-1-1-1-2-221111-1-11111-1-10000-2-2220000i3i3−i3−i3i3i3−i3−i311-1-111-1-1−i3−i3i3i3i3i3−i3−i30000000000
χ352222-2-2-12-2-22-2-2-1-1-1111122-211-1-1-1-111-1-111000000002i2i−2i−2i−i3−i3i3i3i3i3−i3−i333−3−3−3−333−i−iii−i−iii0000000000
χ362222-2-2-12-2-22-2-2-1-1-1111122-211-1-1-1-111-1-111000000002i2i−2i−2ii3i3−i3−i3−i3−i3i3i3−3−33333−3−3−i−iii−i−iii0000000000
χ372222-2-2-12-2-22-2-2-1-1-1111122-211-1-1-1-111-1-11100000000−2i−2i2i2i−i3−i3i3i3i3i3−i3−i3−3−33333−3−3ii−i−iii−i−i0000000000
χ382222-2-2-12-2-22-2-2-1-1-1111122-211-1-1-1-111-1-11100000000−2i−2i2i2ii3i3−i3−i3−i3−i3i3i333−3−3−3−333ii−i−iii−i−i0000000000
χ392-22-22-22200-22-2-22-200000002-2002-22-20000002i−2i−i2i2−i2i22−22−200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000
χ402-22-22-22200-22-2-22-200000002-2002-22-20000002i−2ii2−i2i2−i2−22−2200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000
χ412-22-22-22200-22-2-22-200000002-2002-22-2000000−2i2i−i2i2−i2i2−22−220000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000
χ422-22-22-22200-22-2-22-200000002-2002-22-2000000−2i2ii2−i2i2−i22−22−20000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i22−22−22−22−20000000000
χ432-22-22-2-1200-22-21-1133−3−3000-113−3-11-113−33−3002i−2i−i2i2−i2i22−22−2−i3i3−i3i3−ii−iiζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ230000000000
χ442-22-22-2-1200-22-21-1133−3−3000-113−3-11-113−33−3002i−2ii2−i2i2−i2−22−22−i3i3−i3i3−ii−ii−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ230000000000
χ452-22-22-2-1200-22-21-1133−3−3000-113−3-11-113−33−300−2i2i−i2i2−i2i2−22−22i3−i3i3−i3i−ii−iζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ230000000000
χ462-22-22-2-1200-22-21-1133−3−3000-113−3-11-113−33−300−2i2ii2−i2i2−i22−22−2i3−i3i3−i3i−ii−i−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ230000000000
χ472-22-22-2-1200-22-21-11−3−333000-11−33-11-11−33−33002i−2i−i2i2−i2i22−22−2i3−i3i3−i3−ii−iiζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ70000000000
χ482-22-22-2-1200-22-21-11−3−333000-11−33-11-11−33−33002i−2ii2−i2i2−i2−22−22i3−i3i3−i3−ii−ii−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ70000000000
χ492-22-22-2-1200-22-21-11−3−333000-11−33-11-11−33−3300−2i2i−i2i2−i2i2−22−22−i3i3−i3i3i−ii−iζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ70000000000
χ502-22-22-2-1200-22-21-11−3−333000-11−33-11-11−33−3300−2i2ii2−i2i2−i22−22−2−i3i3−i3i3i−ii−i−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ70000000000
χ512-22-2-222200-2-22-22-20000000-22002-2-2200002-200−i2i2i2−i2−i2i2i2−i2-222-20000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000
χ522-22-2-222200-2-22-22-20000000-22002-2-2200002-200i2−i2−i2i2i2−i2−i2i2-222-20000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000
χ532-22-2-222200-2-22-22-20000000-22002-2-220000-2200−i2i2i2−i2i2−i2−i2i22-2-220000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000
χ542-22-2-222200-2-22-22-20000000-22002-2-220000-2200i2−i2−i2i2−i2i2i2−i22-2-220000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000
χ552-22-2-22-1200-2-221-1133−3−30001-1−33-111-1−333−32-200−i2i2i2−i2−i2i2i2−i21-1-11−333−3ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ230000000000
χ562-22-2-22-1200-2-221-1133−3−30001-1−33-111-1−333−32-200i2−i2−i2i2i2−i2−i2i21-1-11−333−3−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ230000000000
χ572-22-2-22-1200-2-221-1133−3−30001-1−33-111-1−333−3-2200−i2i2i2−i2i2−i2−i2i2-111-13−3−33ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ230000000000
χ582-22-2-22-1200-2-221-1133−3−30001-1−33-111-1−333−3-2200i2−i2−i2i2−i2i2i2−i2-111-13−3−33−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ230000000000
χ592-22-2-22-1200-2-221-11−3−3330001-13−3-111-13−3−332-200−i2i2i2−i2−i2i2i2−i21-1-113−3−33ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ70000000000
χ602-22-2-22-1200-2-221-11−3−3330001-13−3-111-13−3−332-200i2−i2−i2i2i2−i2−i2i21-1-113−3−33−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ70000000000
χ612-22-2-22-1200-2-221-11−3−3330001-13−3-111-13−3−33-2200−i2i2i2−i2i2−i2−i2i2-111-1−333−3ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ70000000000
χ622-22-2-22-1200-2-221-11−3−3330001-13−3-111-13−3−33-2200i2−i2−i2i2−i2i2i2−i2-111-1−333−3−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ70000000000
χ63444444-2-444-4-4-4-2-2-2-2-2-2-24-4-4-2-2-2-2222222220000000000000000000000000000000000000000000000
χ64444444-2-4-4-4-4-4-4-2-2-22222-444-2-2222222-2-2-2-20000000000000000000000000000000000000000000000
χ654444-4-4-2-444-444-2-2-2-2-2-2-2-44-4222222-2-2-2-2220000000000000000000000000000000000000000000000
χ664444-4-4-2-4-4-4-444-2-2-222224-4422-2-222-2-222-2-20000000000000000000000000000000000000000000000
χ6744-4-400404-40004-4-44-44-400000000000000000000000000000000000000000000000000000−2i22i2000000
χ6844-4-400404-40004-4-44-44-4000000000000000000000000000000000000000000000000000002i2−2i2000000
χ6944-4-40040-440004-4-4-44-44000000000000000000000000000000000000000000000000000−2i22i200000000
χ7044-4-40040-440004-4-4-44-440000000000000000000000000000000000000000000000000002i2−2i200000000
χ714-44-44-44-4004-44-44-400000004-400-44-4400000000000000000000000000000000000000000000000000
χ724-44-44-4-2-4004-442-222323−23−23000-2223−232-22-2−2323−23230000000000000000000000000000000000000000000000
χ734-44-44-4-2-4004-442-22−23−232323000-22−23232-22-223−2323−230000000000000000000000000000000000000000000000
χ744-44-4-444-40044-4-44-40000000-4400-444-400000000000000000000000000000000000000000000000000
χ754-44-4-44-2-40044-42-222323−23−230002-2−23232-2-2223−23−23230000000000000000000000000000000000000000000000
χ764-44-4-44-2-40044-42-22−23−2323230002-223−232-2-22−232323−230000000000000000000000000000000000000000000000
χ7788-8-800-408-8000-444-44-440000000000000000000000000000000000000000000000000000000000000
χ7888-8-800-40-88000-4444-44-40000000000000000000000000000000000000000000000000000000000000
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.