Finite Group Databasebeta

← Group #10699224

Character table — Group #10699224

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888888888888888824242424484848484848
order12222234444446661212121244466121212121212121212128888888888882424242424242424242424242424242424242424242424244444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
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
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ922222222-222-22222-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2-20000000000000000000000002222-2-2-2-20000000000
χ1022222222-222-22222-2-2-2-2-2-2-22222-2-2-2-2-2-222-2-222000000000000000000000000-2-2-2-222220000000000
χ112222222-22-2-22-222222222-2-222-2-222-2-2-2-2-2-20000000000000000000000000000000000000000002-200
χ122222222-22-2-22-222222222-2-222-2-222-2-2-2-2-2-2000000000000000000000000000000000000000000-2200
χ132222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000000000002i−2i
χ142222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-2-22222-2-200000000000000000000000000000000000000000000−2i2i
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
χ16222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-10000000000
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
χ18222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2222211111111-1-1-1-1-1-1-1-1111111110000000000
χ19222222-12-222-22-1-1-11111-2-2-2-1-1-1-1111111-1-122-2-20000000033−3−333−3−33333−3−3−3−3-1-1-1-111110000000000
χ20222222-12-222-22-1-1-11111-2-2-2-1-1-1-1111111-1-122-2-200000000−3−333−3−333−3−3−3−33333-1-1-1-111110000000000
χ21222222-12-222-22-1-1-11111-2-2-2-1-1-1-1111111-1-1-2-2220000000033−3−333−3−3−3−3−3−333331111-1-1-1-10000000000
χ22222222-12-222-22-1-1-11111-2-2-2-1-1-1-1111111-1-1-2-22200000000−3−333−3−3333333−3−3−3−31111-1-1-1-10000000000
χ232222-2-2222-2-2222222222-22-2-2-222-2-222-2-2-2-200000000000000000000000000000000000000002-20000
χ242222-2-2222-2-2222222222-22-2-2-222-2-222-2-2-2-20000000000000000000000000000000000000000-220000
χ252222-2-222-2-2-2-22222-2-2-2-22-22-2-22222-2-222-2-20000000000000000000000000000000000002i2i−2i−2i000000
χ262222-2-222-2-2-2-22222-2-2-2-22-22-2-22222-2-222-2-2000000000000000000000000000000000000−2i−2i2i2i000000
χ272222-2-22-22222-22222222-2-22-2-2-2-2-2-2-2-22222000022-2-200002222-2-2-2-200000000000000000000000000
χ282222-2-22-22222-22222222-2-22-2-2-2-2-2-2-2-222220000-2-2220000-2-2-2-2222200000000000000000000000000
χ292222-2-22-2-222-2-2222-2-2-2-222-2-2-2-2-22222-2-222000000002i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ302222-2-22-2-222-2-2222-2-2-2-222-2-2-2-2-22222-2-22200000000−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ312222-2-2-1-22222-2-1-1-1-1-1-1-1-2-2211111111-1-1-1-1000022-2-20000-1-1-1-11111−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000
χ322222-2-2-1-22222-2-1-1-1-1-1-1-1-2-2211111111-1-1-1-1000022-2-20000-1-1-1-11111i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000
χ332222-2-2-1-22222-2-1-1-1-1-1-1-1-2-2211111111-1-1-1-10000-2-22200001111-1-1-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000
χ342222-2-2-1-22222-2-1-1-1-1-1-1-1-2-2211111111-1-1-1-10000-2-22200001111-1-1-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000
χ352222-2-2-1-2-222-2-2-1-1-1111122-21111-1-1-1-111-1-1000000002i2i−2i−2i33−3−3−3−333−i−iii−i−iii−i3−i3i3i3i3i3−i3−i30000000000
χ362222-2-2-1-2-222-2-2-1-1-1111122-21111-1-1-1-111-1-1000000002i2i−2i−2i−3−33333−3−3−i−iii−i−iiii3i3−i3−i3−i3−i3i3i30000000000
χ372222-2-2-1-2-222-2-2-1-1-1111122-21111-1-1-1-111-1-100000000−2i−2i2i2i33−3−3−3−333ii−i−iii−i−ii3i3−i3−i3−i3−i3i3i30000000000
χ382222-2-2-1-2-222-2-2-1-1-1111122-21111-1-1-1-111-1-100000000−2i−2i2i2i−3−33333−3−3ii−i−iii−i−i−i3−i3i3i3i3i3−i3−i30000000000
χ392-2-222-22-202-2022-2-200000002-22-20000002-2002-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200002-22-20000000000
χ402-2-222-22-202-2022-2-200000002-22-20000002-2002-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200002-22-20000000000
χ412-2-222-22-202-2022-2-200000002-22-20000002-200-22−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000-22-220000000000
χ422-2-222-22-202-2022-2-200000002-22-20000002-200-22i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000-22-220000000000
χ432-2-222-2-1-202-202-1113−33−3000-11-113−33−33−3-11002-2−i2i2−i2i2−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ73−33−3-11-110000000000
χ442-2-222-2-1-202-202-1113−33−3000-11-113−33−33−3-11002-2i2−i2i2−i2i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ73−33−3-11-110000000000
χ452-2-222-2-1-202-202-1113−33−3000-11-113−33−33−3-1100-22−i2i2−i2i2i2−i2i2−i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−33−331-11-10000000000
χ462-2-222-2-1-202-202-1113−33−3000-11-113−33−33−3-1100-22i2−i2i2−i2−i2i2−i2i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−33−331-11-10000000000
χ472-2-222-2-1-202-202-111−33−33000-11-11−33−33−33-11002-2−i2i2−i2i2−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−33−33-11-110000000000
χ482-2-222-2-1-202-202-111−33−33000-11-11−33−33−33-11002-2i2−i2i2−i2i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−33−33-11-110000000000
χ492-2-222-2-1-202-202-111−33−33000-11-11−33−33−33-1100-22−i2i2−i2i2i2−i2i2−i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ233−33−31-11-10000000000
χ502-2-222-2-1-202-202-111−33−33000-11-11−33−33−33-1100-22i2−i2i2−i2−i2i2−i2i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ233−33−31-11-10000000000
χ512-2-22-222202-20-22-2-20000000-22-220000002-22i−2i00−i2i2i2−i22−2−22−i2i2−i2i2i2−i2i2−i22−2−222−2−222i−2i−2i2i00000000000000
χ522-2-22-222202-20-22-2-20000000-22-220000002-22i−2i00i2−i2−i2i2−222−2i2−i2i2−i2−i2i2−i2i2−222−2−222−22i−2i−2i2i00000000000000
χ532-2-22-222202-20-22-2-20000000-22-220000002-2−2i2i00−i2i2i2−i2−222−2−i2i2−i2i2i2−i2i2−i2−222−2−222−2−2i2i2i−2i00000000000000
χ542-2-22-222202-20-22-2-20000000-22-220000002-2−2i2i00i2−i2−i2i22−2−22i2−i2i2−i2−i2i2−i2i22−2−222−2−22−2i2i2i−2i00000000000000
χ552-2-22-22-1202-20-2-1113−33−30001-11-1−33−333−3-112i−2i00−i2i2i2−i22−2−22ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−iii−i−i3i3i3−i30000000000
χ562-2-22-22-1202-20-2-1113−33−30001-11-1−33−333−3-112i−2i00i2−i2−i2i2−222−2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−iii−i−i3i3i3−i30000000000
χ572-2-22-22-1202-20-2-1113−33−30001-11-1−33−333−3-11−2i2i00−i2i2i2−i2−222−2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7i−i−iii3−i3−i3i30000000000
χ582-2-22-22-1202-20-2-1113−33−30001-11-1−33−333−3-11−2i2i00i2−i2−i2i22−2−22−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7i−i−iii3−i3−i3i30000000000
χ592-2-22-22-1202-20-2-111−33−330001-11-13−33−3−33-112i−2i00−i2i2i2−i22−2−22ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−iii−ii3−i3−i3i30000000000
χ602-2-22-22-1202-20-2-111−33−330001-11-13−33−3−33-112i−2i00i2−i2−i2i2−222−2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−iii−ii3−i3−i3i30000000000
χ612-2-22-22-1202-20-2-111−33−330001-11-13−33−3−33-11−2i2i00−i2i2i2−i2−222−2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23i−i−ii−i3i3i3−i30000000000
χ622-2-22-22-1202-20-2-111−33−330001-11-13−33−3−33-11−2i2i00i2−i2−i2i22−2−22−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23i−i−ii−i3i3i3−i30000000000
χ63444444-2-44-4-44-4-2-2-2-2-2-2-24-4-4-2-222-2-22222220000000000000000000000000000000000000000000000
χ64444444-2-4-4-4-4-4-4-2-2-22222-444-2-22222-2-2-2-2220000000000000000000000000000000000000000000000
χ654444-4-4-244-4-444-2-2-2-2-2-2-2-44-422-2-222-2-222220000000000000000000000000000000000000000000000
χ664444-4-4-24-4-4-4-44-2-2-222224-4422-2-2-2-222-2-2220000000000000000000000000000000000000000000000
χ6744-4-40040400-40-44-444-4-40000000000000000000000000000000000000000000000000002-22-2000000
χ6844-4-40040400-40-44-444-4-4000000000000000000000000000000000000000000000000000-22-22000000
χ6944-4-40040-40040-44-4-4-4440000000000000000000000000000000000000000000000000002i−2i−2i2i000000
χ7044-4-40040-40040-44-4-4-444000000000000000000000000000000000000000000000000000−2i2i2i−2i000000
χ714-4-444-4440-440-44-4-400000004-4-44000000-440000000000000000000000000000000000000000000000
χ724-4-444-4-240-440-4-22223−2323−23000-222-223−23−2323−23232-20000000000000000000000000000000000000000000000
χ734-4-444-4-240-440-4-222−2323−2323000-222-2−232323−2323−232-20000000000000000000000000000000000000000000000
χ744-4-44-444-40-44044-4-40000000-444-4000000-440000000000000000000000000000000000000000000000
χ754-4-44-44-2-40-4404-22223−2323−230002-2-22−232323−23−23232-20000000000000000000000000000000000000000000000
χ764-4-44-44-2-40-4404-222−2323−23230002-2-2223−23−232323−232-20000000000000000000000000000000000000000000000
χ7788-8-800-40800-804-44-4-4440000000000000000000000000000000000000000000000000000000000000
χ7888-8-800-40-800804-4444-4-40000000000000000000000000000000000000000000000000000000000000
χ798-88-8008000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ808-88-800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000
χ818-88-800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000

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