Finite Group Databasebeta

← Group #72341780

Character table — Group #72341780

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size11112233336666666666666612121616242424242424242424242424242424243232323248484848484848484848646464646464
order1222442222222222224444444444888888888888888836664444444444121212121212
χ11111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111111
χ311111111111111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1
χ51-11-1-1111-1-11111-1-1-1-1-1-1-11111-1i−i11-1-1111111-1-1-1-1-1-11-11-1i−ii−ii−iii−i−i1-1ii−i−i
χ61-11-1-1111-1-11111-1-1-1-1-1-1-11111-1i−i-1-111-1-1-1-1-1-11111111-11-1−iii−i−ii−i−iii1-1ii−i−i
χ71-11-1-1111-1-11111-1-1-1-1-1-1-11111-1−ii11-1-1111111-1-1-1-1-1-11-11-1−ii−ii−ii−i−iii1-1−i−iii
χ81-11-1-1111-1-11111-1-1-1-1-1-1-11111-1−ii-1-111-1-1-1-1-1-11111111-11-1i−i−iii−iii−i−i1-1−i−iii
χ922222222222222222222222222220000000000000000-1-1-1-10022000000-1-1-1-1-1-1
χ1022222222222222222222222222-2-20000000000000000-1-1-1-100-2-2000000-1-11111
χ112222-2-2222222222222-2-2-2-2-2-2-2-200000000000000000022220000000000-2-20000
χ122222-2-2222222222222-2-2-2-2-2-2-2-2000000000000000000-1-1-1-1000000000011−i3i3−i3i3
χ132222-2-2222222222222-2-2-2-2-2-2-2-2000000000000000000-1-1-1-1000000000011i3−i3i3−i3
χ1422-2-2002-22-222-2-222-2-20000000000−i2i2−i2i2−i2−i2−i2i2i2i2−i2−i2−i2i2i2i22-2-220000000000000000
χ1522-2-2002-22-222-2-222-2-20000000000i2−i2i2−i2i2i2i2−i2−i2−i2i2i2i2−i2−i2−i22-2-220000000000000000
χ162-22-22-222-2-22222-2-2-2-2222-2-2-2-220000000000000000002-22-20000000000-220000
χ172-22-22-222-2-22222-2-2-2-2222-2-2-2-22000000000000000000-11-1100000000001-13−3−33
χ182-22-22-222-2-22222-2-2-2-2222-2-2-2-22000000000000000000-11-1100000000001-1−333−3
χ192-22-2-2222-2-22222-2-2-2-2-2-2-22222-22i−2i0000000000000000-11-11002i−2i000000-11−i−iii
χ202-22-2-2222-2-22222-2-2-2-2-2-2-22222-2−2i2i0000000000000000-11-1100−2i2i000000-11ii−i−i
χ212-2-22002-2-2222-2-2-2-2220000000000−i2i2i2−i2−i2−i2−i2i2i2i2i2i2i2−i2−i2−i222-2-20000000000000000
χ222-2-22002-2-2222-2-2-2-2220000000000i2−i2−i2i2i2i2i2−i2−i2−i2−i2−i2−i2i2i2i222-2-20000000000000000
χ233333333333-1-1-1-1-1-1-1-13-1-13-1-1-1-13311111-1-11-1-11-1-11-1-1000011-1-111-1-1-1-1000000
χ243333333333-1-1-1-1-1-1-1-13-1-13-1-1-1-133-1-1-1-1-111-111-111-1110000-1-1-1-1-1-11111000000
χ253333333333-1-1-1-1-1-1-1-13-1-13-1-1-1-1-3-311111-1-11-1-11-1-11-1-10000-1-111-1-11111000000
χ263333333333-1-1-1-1-1-1-1-13-1-13-1-1-1-1-3-3-1-1-1-1-111-111-111-1110000111111-1-1-1-1000000
χ273-33-3-3333-3-3-1-1-1-11111-3113-1-1-113i−3i11-1-11-1-11-1-1-111-1110000i−i−iii−i−i−iii000000
χ283-33-3-3333-3-3-1-1-1-11111-3113-1-1-113i−3i-1-111-111-1111-1-11-1-10000−ii−ii−iiii−i−i000000
χ293-33-3-3333-3-3-1-1-1-11111-3113-1-1-11−3i3i11-1-11-1-11-1-1-111-1110000−iii−i−iiii−i−i000000
χ303-33-3-3333-3-3-1-1-1-11111-3113-1-1-11−3i3i-1-111-111-1111-1-11-1-10000i−ii−ii−i−i−iii000000
χ3144-4-4004-44-444-4-444-4-400000000000000000000000000-222-20000000000000000
χ324-4-44004-4-4444-4-4-4-44400000000000000000000000000-2-2220000000000000000
χ33666666-2-2-2-22-22-22-22-2-222-222-2-2002222-200-200-200-20000000000000000000000
χ34666666-2-2-2-22-22-22-22-2-222-222-2-200-2-2-2-220020020020000000000000000000000
χ35666666-2-2-2-2-22-22-22-22-2-2-2-2-2-22200000000000000000000002200-2-20000000000
χ36666666-2-2-2-2-22-22-22-22-2-2-2-2-2-2220000000000000000000000-2-200220000000000
χ376666-6-66666-2-2-2-2-2-2-2-2-622-6222200000000000000000000000000000000000000
χ386666-6-6-2-2-2-22-22-22-22-22-2-22-2-22200000002i−2i02i−2i02i−2i02i−2i00000000000000000000
χ396666-6-6-2-2-2-22-22-22-22-22-2-22-2-2220000000−2i2i0−2i2i0−2i2i0−2i2i00000000000000000000
χ406666-6-6-2-2-2-2-22-22-22-22222222-2-200000000000000000000000000002-22-2000000
χ416666-6-6-2-2-2-2-22-22-22-22222222-2-20000000000000000000000000000-22-22000000
χ4266-6-6006-66-6-2-222-2-2220000000000−i2i2−i2i2−i2i2i2i2−i2−i2−i2i2i2i2−i2−i200000000000000000000
χ4366-6-6006-66-6-2-222-2-2220000000000i2−i2i2−i2i2−i2−i2−i2i2i2i2−i2−i2−i2i2i200000000000000000000
χ4466-6-600-22-222-2-222-2-2204i−4i04i−4i0000−i2i2−i2i2i22−2−i2−22i22−2−i2−2200000000000000000000
χ4566-6-600-22-222-2-222-2-2204i−4i04i−4i0000i2−i2i2−i2−i2−22i22−2−i2−22i22−200000000000000000000
χ4666-6-600-22-222-2-222-2-220−4i4i0−4i4i0000−i2i2−i2i2i2−22−i22−2i2−22−i22−200000000000000000000
χ4766-6-600-22-222-2-222-2-220−4i4i0−4i4i0000i2−i2i2−i2−i22−2i2−22−i22−2i2−2200000000000000000000
χ486-66-66-666-6-6-2-2-2-222226-2-2-6222-200000000000000000000000000000000000000
χ496-66-66-6-2-2222-22-2-22-22-2222-2-22-200000002i−2i02i−2i0−2i2i0−2i2i00000000000000000000
χ506-66-66-6-2-2222-22-2-22-22-2222-2-22-20000000−2i2i0−2i2i02i−2i02i−2i00000000000000000000
χ516-66-66-6-2-222-22-222-22-2-2-2-2222-2200000000000000000000000000002i−2i−2i2i000000
χ526-66-66-6-2-222-22-222-22-2-2-2-2222-220000000000000000000000000000−2i2i2i−2i000000
χ536-66-6-66-2-2222-22-2-22-222-2-2-222-220022-2-2-200-20020020000000000000000000000
χ546-66-6-66-2-2222-22-2-22-222-2-2-222-2200-2-222200200-200-20000000000000000000000
χ556-66-6-66-2-222-22-222-22-2222-2-2-22-200000000000000000000002i−2i00−2i2i0000000000
χ566-66-6-66-2-222-22-222-22-2222-2-2-22-20000000000000000000000−2i2i002i−2i0000000000
χ576-6-66006-6-66-2-22222-2-20000000000−i2i2i2−i2−i2i2i2i2−i2−i2i2−i2−i2−i2i2i200000000000000000000
χ586-6-66006-6-66-2-22222-2-20000000000i2−i2−i2i2i2−i2−i2−i2i2i2−i2i2i2i2−i2−i200000000000000000000
χ596-6-6600-222-22-2-22-222-204i−4i0−4i4i0000−i2i2i2−i2i2−22−i22−2−i22−2i2−2200000000000000000000
χ606-6-6600-222-22-2-22-222-204i−4i0−4i4i0000i2−i2−i2i2−i22−2i2−22i2−22−i22−200000000000000000000
χ616-6-6600-222-22-2-22-222-20−4i4i04i−4i0000−i2i2i2−i2i22−2−i2−22−i2−22i22−200000000000000000000
χ626-6-6600-222-22-2-22-222-20−4i4i04i−4i0000i2−i2−i2i2−i2−22i22−2i22−2−i2−2200000000000000000000
χ631212-12-1200-44-44-444-4-444-40000000000000000000000000000000000000000000000
χ6412-12-121200-444-4-444-44-4-440000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).