Finite Group Databasebeta

← Group #10693213

Character table — Group #10693213

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888888888888888888888888888824242424484848484848
order1222223446661212121222444668888121224242424242424242444666688888812121212121212122424242424242424242424242222448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ611111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ711111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-111
χ811111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ91111-1-11-1-1111-1-1-1-11-111-1-1-1ii−i−i11iiii−i−i−i−i11-1-11-111i−iii−i−i11-1-11-1-1-1ii−i−iiiii−i−i−i−i11-1-1i−i1-1i−i
χ101111-1-11-1-1111-1-1-1-11-111-1-1-1ii−i−i11iiii−i−i−i−i11-1-11-111i−iii−i−i11-1-11-1-1-1ii−i−iiiii−i−i−i−i-1-111−ii-11−ii
χ111111-1-11-1-1111-1-1-1-11-111-1-1-1ii−i−i11iiii−i−i−i−i-1-1111-1-1-1i−i−i−iii-1-1111-111ii−i−i−i−i−i−iiiii11-1-1i−i-11−ii
χ121111-1-11-1-1111-1-1-1-11-111-1-1-1ii−i−i11iiii−i−i−i−i-1-1111-1-1-1i−i−i−iii-1-1111-111ii−i−i−i−i−i−iiiii-1-111−ii1-1i−i
χ131111-1-11-1-1111-1-1-1-11-111-1-1-1−i−iii11−i−i−i−iiiii11-1-11-111−ii−i−iii11-1-11-1-1-1−i−iii−i−i−i−iiiii11-1-1−ii1-1−ii
χ141111-1-11-1-1111-1-1-1-11-111-1-1-1−i−iii11−i−i−i−iiiii11-1-11-111−ii−i−iii11-1-11-1-1-1−i−iii−i−i−i−iiiii-1-111i−i-11i−i
χ151111-1-11-1-1111-1-1-1-11-111-1-1-1−i−iii11−i−i−i−iiiii-1-1111-1-1-1−iiii−i−i-1-1111-111−i−iiiiiii−i−i−i−i11-1-1−ii-11i−i
χ161111-1-11-1-1111-1-1-1-11-111-1-1-1−i−iii11−i−i−i−iiiii-1-1111-1-1-1−iiii−i−i-1-1111-111−i−iiiiiii−i−i−i−i-1-111i−i1-1−ii
χ172222222222222222-2-22-2-222222222222222220000-2-200-2-200000000-2-200-2-2-2-2000000000000000000
χ182222222222222222-2-22-2-222-2-2-2-222-2-2-2-2-2-2-2-20000-2-2002200000000-2-2002222000000000000000000
χ192222222-2-2222-2-2-2-222-2-2-2220000-2-20000000000002200002i−2i2i−2i0000-2-20000002i2i−2i−2i2i2i−2i−2i0000000000
χ202222222-2-2222-2-2-2-222-2-2-2220000-2-2000000000000220000−2i2i−2i2i0000-2-2000000−2i−2i2i2i−2i−2i2i2i0000000000
χ212222222-2-2222-2-2-2-2-2-2-222220000-2-2000000002-22-2-2-222000000-2-22222-2-20000000000000000000000
χ222222222-2-2222-2-2-2-2-2-2-222220000-2-200000000-22-22-2-2-2-200000022-2-222220000000000000000000000
χ23222222-122-1-1-1-1-1-1-122222-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ24222222-122-1-1-1-1-1-1-122222-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11122-2-2-2-21111-1-111-1-1-1-1111111110000000000
χ25222222-122-1-1-1-1-1-1-122222-1-1-2-2-2-2-1-1111111112222-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111110000000000
χ26222222-122-1-1-1-1-1-1-122222-1-1-2-2-2-2-1-111111111-2-2-2-2-1-111-2-222221111-1-1111111-1-1-1-1-1-1-1-10000000000
χ27222222-122-1-1-1-1-1-1-1-2-22-2-2-1-12222-1-1-1-1-1-1-1-1-1-1000011−i3i3-2-20000−i3i3−i3i311−i3i31111−i3i3−i3i3−i3i3−i3i30000000000
χ28222222-122-1-1-1-1-1-1-1-2-22-2-2-1-12222-1-1-1-1-1-1-1-1-1-1000011i3−i3-2-20000i3−i3i3−i311i3−i31111i3−i3i3−i3i3−i3i3−i30000000000
χ29222222-122-1-1-1-1-1-1-1-2-22-2-2-1-1-2-2-2-2-1-111111111000011−i3i3220000−i3i3−i3i311−i3i3-1-1-1-1i3−i3i3−i3i3−i3i3−i30000000000
χ30222222-122-1-1-1-1-1-1-1-2-22-2-2-1-1-2-2-2-2-1-111111111000011i3−i3220000i3−i3i3−i311i3−i3-1-1-1-1−i3i3−i3i3−i3i3−i3i30000000000
χ31222222-1-2-2-1-1-1111122-2-2-2-1-100001133−3−333−3−30000-1-1−i3i3002i−2i2i−2ii3−i3−i3i311i3−i33−33−3−i−iii−i−iii0000000000
χ32222222-1-2-2-1-1-1111122-2-2-2-1-100001133−3−333−3−30000-1-1i3−i300−2i2i−2i2i−i3i3i3−i311−i3i33−33−3ii−i−iii−i−i0000000000
χ33222222-1-2-2-1-1-1111122-2-2-2-1-1000011−3−333−3−3330000-1-1−i3i300−2i2i−2i2ii3−i3−i3i311i3−i3−33−33ii−i−iii−i−i0000000000
χ34222222-1-2-2-1-1-1111122-2-2-2-1-1000011−3−333−3−3330000-1-1i3−i3002i−2i2i−2i−i3i3i3−i311−i3i3−33−33−i−iii−i−iii0000000000
χ35222222-1-2-2-1-1-11111-2-2-222-1-100001133−3−333−3−32-22-211-1-100000011-1-1-1-111−33−333−3−333−3−330000000000
χ36222222-1-2-2-1-1-11111-2-2-222-1-100001133−3−333−3−3-22-221111000000-1-111-1-1-1-1−33−33−333−3−333−30000000000
χ37222222-1-2-2-1-1-11111-2-2-222-1-1000011−3−333−3−3332-22-211-1-100000011-1-1-1-1113−33−3−333−3−333−30000000000
χ38222222-1-2-2-1-1-11111-2-2-222-1-1000011−3−333−3−333-22-221111000000-1-111-1-1-1-13−33−33−3−333−3−330000000000
χ392222-2-222222222222-2-2-22-2-20000-2-20000000000002-200002-2-220000-2200000022-2-2-2-2220000000000
χ402222-2-222222222222-2-2-22-2-20000-2-20000000000002-20000-222-20000-22000000-2-22222-2-20000000000
χ412222-2-22222222222-22-22-2-2-20000-2-2000000002-2-22-2222000000-2-2-2-22-2220000000000000000000000
χ422222-2-22222222222-22-22-2-2-20000-2-200000000-222-2-22-2-200000022222-2-2-20000000000000000000000
χ432222-2-22-2-2222-2-2-2-2-222-22-2-22i2i−2i−2i222i2i2i2i−2i−2i−2i−2i0000-2200−2i2i00000000-2200−2i−2i2i2i000000000000000000
χ442222-2-22-2-2222-2-2-2-2-222-22-2-2−2i−2i2i2i22−2i−2i−2i−2i2i2i2i2i0000-22002i−2i00000000-22002i2i−2i−2i000000000000000000
χ452222-2-2-122-1-1-1-1-1-1-12-2-2-2211000011−i3−i3i3i3i3i3−i3−i30000-11−i3i3002-2-22i3−i3i3−i31-1−i3i3−i3i3i3−i3-1-11111-1-10000000000
χ462222-2-2-122-1-1-1-1-1-1-12-2-2-2211000011−i3−i3i3i3i3i3−i3−i30000-11i3−i300-222-2−i3i3−i3i31-1i3−i3−i3i3i3−i311-1-1-1-1110000000000
χ472222-2-2-122-1-1-1-1-1-1-12-2-2-2211000011i3i3−i3−i3−i3−i3i3i30000-11−i3i300-222-2i3−i3i3−i31-1−i3i3i3−i3−i3i311-1-1-1-1110000000000
χ482222-2-2-122-1-1-1-1-1-1-12-2-2-2211000011i3i3−i3−i3−i3−i3i3i30000-11i3−i3002-2-22−i3i3−i3i31-1i3−i3i3−i3−i3i3-1-11111-1-10000000000
χ492222-2-2-122-1-1-1-1-1-1-1-22-22-211000011−i3−i3i3i3i3i3−i3−i32-2-221-1-1-10000001111-11-1-1i3−i3−i3i3−i3i3i3−i3i3−i3−i3i30000000000
χ502222-2-2-122-1-1-1-1-1-1-1-22-22-211000011−i3−i3i3i3i3i3−i3−i3-222-21-111000000-1-1-1-1-1111i3−i3−i3i3i3−i3−i3i3−i3i3i3−i30000000000
χ512222-2-2-122-1-1-1-1-1-1-1-22-22-211000011i3i3−i3−i3−i3−i3i3i32-2-221-1-1-10000001111-11-1-1−i3i3i3−i3i3−i3−i3i3−i3i3i3−i30000000000
χ522222-2-2-122-1-1-1-1-1-1-1-22-22-211000011i3i3−i3−i3−i3−i3i3i3-222-21-111000000-1-1-1-1-1111−i3i3i3−i3−i3i3i3−i3i3−i3−i3i30000000000
χ532222-2-2-1-2-2-1-1-111112-222-2112i2i−2i−2i-1-1−i−i−i−iiiii22-2-2-11-1-12i−2i2i2i−2i−2i-1-111-1111−i−iii−i−i−i−iiiii0000000000
χ542222-2-2-1-2-2-1-1-111112-222-2112i2i−2i−2i-1-1−i−i−i−iiiii-2-222-11112i−2i−2i−2i2i2i11-1-1-11-1-1−i−iiiiiii−i−i−i−i0000000000
χ552222-2-2-1-2-2-1-1-111112-222-211−2i−2i2i2i-1-1iiii−i−i−i−i22-2-2-11-1-1−2i2i−2i−2i2i2i-1-111-1111ii−i−iiiii−i−i−i−i0000000000
χ562222-2-2-1-2-2-1-1-111112-222-211−2i−2i2i2i-1-1iiii−i−i−i−i-2-222-1111−2i2i2i2i−2i−2i11-1-1-11-1-1ii−i−i−i−i−i−iiiii0000000000
χ572222-2-2-1-2-2-1-1-11111-222-22112i2i−2i−2i-1-1−i−i−i−iiiii00001-1−i3i3−2i2i0000−i3i3i3−i31-1i3−i3ii−i−i3−33−3−33−330000000000
χ582222-2-2-1-2-2-1-1-11111-222-22112i2i−2i−2i-1-1−i−i−i−iiiii00001-1i3−i3−2i2i0000i3−i3−i3i31-1−i3i3ii−i−i−33−333−33−30000000000
χ592222-2-2-1-2-2-1-1-11111-222-2211−2i−2i2i2i-1-1iiii−i−i−i−i00001-1−i3i32i−2i0000−i3i3i3−i31-1i3−i3−i−iii−33−333−33−30000000000
χ602222-2-2-1-2-2-1-1-11111-222-2211−2i−2i2i2i-1-1iiii−i−i−i−i00001-1i3−i32i−2i0000i3−i3−i3i31-1−i3i3−i−iii3−33−3−33−330000000000
χ6144-4-44-44004-4-40000000004-4−2i22i2−2i22i200−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000000000000000
χ6244-4-44-44004-4-40000000004-42i2−2i22i2−2i2002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000000000000000
χ6344-4-44-4-200-2222323−23−2300000-22−2i22i2−2i22i223−232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300000000000000000000000000000000000000000000
χ6444-4-44-4-200-2222323−23−2300000-222i2−2i22i2−2i223−23−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000000000000000000000000000000000
χ6544-4-44-4-200-222−23−23232300000-22−2i22i2−2i22i2−23232ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000000000000000000000
χ6644-4-44-4-200-222−23−23232300000-222i2−2i22i2−2i2−2323−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000000000000000000000
χ6744-4-4-444004-4-4000000000-4422−22−22220022−2222−22−2222−222200000000000000000000000000000000000000000000
χ6844-4-4-444004-4-4000000000-44−222222−2200−2222−222222−2222−2200000000000000000000000000000000000000000000
χ6944-4-4-44-200-2222323−23−23000002-222−22−2222−23232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2300000000000000000000000000000000000000000000
χ7044-4-4-44-200-2222323−23−23000002-2−222222−22−2323−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2300000000000000000000000000000000000000000000
χ7144-4-4-44-200-222−23−232323000002-222−22−222223−232ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ700000000000000000000000000000000000000000000
χ7244-4-4-44-200-222−23−232323000002-2−222222−2223−23−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ72ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ700000000000000000000000000000000000000000000
χ734-4-440044-4-4-444-44-400000000000000000000000000000000000000000000000000000002-22-2000000
χ744-4-440044-4-4-444-44-40000000000000000000000000000000000000000000000000000000-22-22000000
χ754-4-44004-44-4-44-44-4400000000000000000000000000000000000000000000000000000002-2-22000000
χ764-4-44004-44-4-44-44-440000000000000000000000000000000000000000000000000000000-222-2000000
χ778-88-800800-88-8000000000000000000000000000000000000000000000000000000000000000000000
χ788-88-800-4004-4443−43−434300000000000000000000000000000000000000000000000000000000000000000
χ798-88-800-4004-44−434343−4300000000000000000000000000000000000000000000000000000000000000000
χ808-8-8800-48-844-4-44-4400000000000000000000000000000000000000000000000000000000000000000
χ818-8-8800-4-8844-44-44-400000000000000000000000000000000000000000000000000000000000000000

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