Finite Group Databasebeta

← Group #72215118

Character table — Group #72215118

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size11112233336666666666888812121212242424243232323232323232323232323232323248484848484848484848484848484848
order1244242244244444444488884444888836661212121224242424242424248888888888888888
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ411111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ511-1-1-1111-1-1-111111-1-1-1-111-1-111-1-111-1-11-1-11-1-1111111-1-1-1-1i−ii−ii−ii−iii−i−iii−i−i
χ611-1-1-1111-1-1-111111-1-1-1-111-1-111-1-111-1-11-1-11-1-1111111-1-1-1-1−ii−ii−ii−ii−i−iii−i−iii
χ711-1-1-1111-1-1-111111-1-1-1-1-1-11111-1-1-1-1111-1-11-1-111-1-1-1-11111i−i−iii−i−iiii−i−i−i−iii
χ811-1-1-1111-1-1-111111-1-1-1-1-1-11111-1-1-1-1111-1-11-1-111-1-1-1-11111−iii−i−iii−i−i−iiiii−i−i
χ922222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1022222222222222222222-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ112222-2-22222-2-2222222220000-2-2-2-200002-2-2222-2-2000000000000000000000000
χ122222-2-22222-2-2222222220000-2-2-2-20000-111-1-1-11133−3−333−3−30000000000000000
χ132222-2-22222-2-2222222220000-2-2-2-20000-111-1-1-111−3−333−3−3330000000000000000
χ1422-2-22-222-2-22-22222-2-2-2-20000-2-22200002222-2-2-2-2000000000000000000000000
χ1522-2-22-222-2-22-22222-2-2-2-20000-2-2220000-1-1-1-1111133−3−3−3−3330000000000000000
χ1622-2-22-222-2-22-22222-2-2-2-20000-2-2220000-1-1-1-11111−3−33333−3−30000000000000000
χ1722-2-2-2222-2-2-222222-2-2-2-222-2-222-2-222-2-2-111-111-1-1-1-1-1-111110000000000000000
χ1822-2-2-2222-2-2-222222-2-2-2-2-2-22222-2-2-2-222-111-111-1-11111-1-1-1-10000000000000000
χ192-22i−2i002-22i−2i0022-2-22i2i−2i−2i2−2−i2i200002−2−i2i2200-22i−2i002−22−2−i2i2−i2i20000000000000000
χ202-22i−2i002-22i−2i0022-2-22i2i−2i−2i2−2−i2i200002−2−i2i2-1−i3i31−ii3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ212-22i−2i002-22i−2i0022-2-22i2i−2i−2i2−2−i2i200002−2−i2i2-1i3−i31−ii−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ222-22i−2i002-22i−2i0022-2-22i2i−2i−2i−22i2−i20000−22i2−i2200-22i−2i00−22−22i2−i2i2−i20000000000000000
χ232-22i−2i002-22i−2i0022-2-22i2i−2i−2i−22i2−i20000−22i2−i2-1−i3i31−ii3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ242-22i−2i002-22i−2i0022-2-22i2i−2i−2i−22i2−i20000−22i2−i2-1i3−i31−ii−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ252-2−2i2i002-2−2i2i0022-2-2−2i−2i2i2i2−2i2−i200002−2i2−i2200-2−2i2i002−22−2i2−i2i2−i20000000000000000
χ262-2−2i2i002-2−2i2i0022-2-2−2i−2i2i2i2−2i2−i200002−2i2−i2-1−i3i31i−i−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ272-2−2i2i002-2−2i2i0022-2-2−2i−2i2i2i2−2i2−i200002−2i2−i2-1i3−i31i−i3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ282-2−2i2i002-2−2i2i0022-2-2−2i−2i2i2i−22−i2i20000−22−i2i2200-2−2i2i00−22−22−i2i2−i2i20000000000000000
χ292-2−2i2i002-2−2i2i0022-2-2−2i−2i2i2i−22−i2i20000−22−i2i2-1−i3i31i−i−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ302-2−2i2i002-2−2i2i0022-2-2−2i−2i2i2i−22−i2i20000−22−i2i2-1i3−i31i−i3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ31333333333333-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-1000000000000000011111111-1-1-1-1-1-1-1-1
χ32333333333333-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-10000000000000000-1-1-1-1-1-1-1-111111111
χ33333333333333-1-1-1-1-1-1-1-1-3-3-3-3-1-1-1-11111000000000000000011-1-111-1-1-1-1-1-11111
χ34333333333333-1-1-1-1-1-1-1-1-3-3-3-3-1-1-1-111110000000000000000-1-111-1-1111111-1-1-1-1
χ3533-3-3-3333-3-3-33-1-1-1-1111133-3-3-1-111-1-1110000000000000000i−ii−ii−ii−i−i−iii−i−iii
χ3633-3-3-3333-3-3-33-1-1-1-1111133-3-3-1-111-1-1110000000000000000−ii−ii−ii−iiii−i−iii−i−i
χ3733-3-3-3333-3-3-33-1-1-1-11111-3-333-1-11111-1-10000000000000000i−i−iii−i−ii−i−iiiii−i−i
χ3833-3-3-3333-3-3-33-1-1-1-11111-3-333-1-11111-1-10000000000000000−iii−i−iii−iii−i−i−i−iii
χ39666666-2-2-2-2-2-22-22-22-22-200002-22-200000000000000000000002200-2-200000000
χ40666666-2-2-2-2-2-22-22-22-22-200002-22-20000000000000000000000-2-2002200000000
χ41666666-2-2-2-2-2-2-22-22-22-220000-22-22000000000000000000002200-2-20000000000
χ42666666-2-2-2-2-2-2-22-22-22-220000-22-2200000000000000000000-2-200220000000000
χ436666-6-66666-6-6-2-2-2-2-2-2-2-200002222000000000000000000000000000000000000
χ446666-6-6-2-2-2-2222-22-22-22-20000-22-22000000000000000000000000000000002i−2i2i−2i
χ456666-6-6-2-2-2-2222-22-22-22-20000-22-2200000000000000000000000000000000−2i2i−2i2i
χ466666-6-6-2-2-2-222-22-22-22-2200002-22-200000000000000000000000000002i−2i2i−2i0000
χ476666-6-6-2-2-2-222-22-22-22-2200002-22-20000000000000000000000000000−2i2i−2i2i0000
χ4866-6-66-666-6-66-6-2-2-2-22222000022-2-2000000000000000000000000000000000000
χ4966-6-66-6-2-222-222-22-2-22-220000-222-2000000000000000000000000000000002-2-22
χ5066-6-66-6-2-222-222-22-2-22-220000-222-200000000000000000000000000000000-222-2
χ5166-6-66-6-2-222-22-22-222-22-200002-2-2200000000000000000000000000002-2-220000
χ5266-6-66-6-2-222-22-22-222-22-200002-2-220000000000000000000000000000-222-20000
χ5366-6-6-66-2-2222-22-22-2-22-2200002-2-2200000000000000000000002i−2i00−2i2i00000000
χ5466-6-6-66-2-2222-22-22-2-22-2200002-2-220000000000000000000000−2i2i002i−2i00000000
χ5566-6-6-66-2-2222-2-22-222-22-20000-222-2000000000000000000002i−2i00−2i2i0000000000
χ5666-6-6-66-2-2222-2-22-222-22-20000-222-200000000000000000000−2i2i002i−2i0000000000
χ576-66i−6i006-66i−6i00-2-222−2i−2i2i2i32−32−3i23i20000−22i2−i200000000000000000000000000000000
χ586-66i−6i006-66i−6i00-2-222−2i−2i2i2i−32323i2−3i200002−2−i2i200000000000000000000000000000000
χ596-6−6i6i006-6−6i6i00-2-2222i2i−2i−2i32−323i2−3i20000−22−i2i200000000000000000000000000000000
χ606-6−6i6i006-6−6i6i00-2-2222i2i−2i−2i−3232−3i23i200002−2i2−i200000000000000000000000000000000
χ6112-1212i−12i00-44−4i4i004-4-444i−4i−4i4i00000000000000000000000000000000000000000000
χ6212-1212i−12i00-44−4i4i00-444-4−4i4i4i−4i00000000000000000000000000000000000000000000
χ6312-12−12i12i00-444i−4i004-4-44−4i4i4i−4i00000000000000000000000000000000000000000000
χ6412-12−12i12i00-444i−4i00-444-44i−4i−4i4i00000000000000000000000000000000000000000000

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