Finite Group Databasebeta

← Group #73124

Character table — Group #73124

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40
size11112222226666888888888888888812122424242424242424
order1222448888224436661212121224242424242424248844448888
χ11111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ4111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ51-1-111-1ii−i−i1-11-11-1-1111-1-1iiii−i−i−i−ii−ii−i1-1i−i1-1
χ61-1-111-1ii−i−i1-11-11-1-1111-1-1iiii−i−i−i−ii−i−ii-11−ii-11
χ71-1-111-1−i−iii1-11-11-1-1111-1-1−i−i−i−iiiii−iii−i-11i−i-11
χ81-1-111-1−i−iii1-11-11-1-1111-1-1−i−i−i−iiiii−ii−ii1-1−ii1-1
χ922222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12200000000
χ10222222-2-2-2-22222-1-1-1-1-1-1-1-111111111-2-200000000
χ112222-2-20000-2-2222222-2-2-2-2000000000000000000
χ122222-2-20000-2-222-1-1-1-1111133−3−333−3−30000000000
χ132222-2-20000-2-222-1-1-1-11111−3−333−3−3330000000000
χ142-2-222-22i2i−2i−2i2-22-2-111-1-1-111−i−i−i−iiiii2i−2i00000000
χ152-2-222-2−2i−2i2i2i2-22-2-111-1-1-111iiii−i−i−i−i−2i2i00000000
χ162-2-22-220000-222-22-2-22-2-222000000000000000000
χ172-2-22-220000-222-2-111-111-1-1−i3−i3i3i3i3i3−i3−i30000000000
χ182-2-22-220000-222-2-111-111-1-1i3i3−i3−i3−i3−i3i3i30000000000
χ193333333333-1-1-1-10000000000000000-1-11111-1-1-1-1
χ203333333333-1-1-1-10000000000000000-1-1-1-1-1-11111
χ21333333-3-3-3-3-1-1-1-100000000000000001111-1-1-1-111
χ22333333-3-3-3-3-1-1-1-1000000000000000011-1-11111-1-1
χ233-3-333-33i3i−3i−3i-11-110000000000000000−iii−i1-1−ii-11
χ243-3-333-33i3i−3i−3i-11-110000000000000000−ii−ii-11i−i1-1
χ253-3-333-3−3i−3i3i3i-11-110000000000000000i−ii−i-11−ii1-1
χ263-3-333-3−3i−3i3i3i-11-110000000000000000i−i−ii1-1i−i-11
χ2744-4-40022−2222−22000011-1-13−33−3ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ230000000000
χ2844-4-40022−2222−22000011-1-1−33−33ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ70000000000
χ2944-4-40022−2222−220000-2-22200002−2−222−2−220000000000
χ3044-4-400−2222−2222000011-1-13−33−3−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ230000000000
χ3144-4-400−2222−2222000011-1-1−33−33−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ70000000000
χ3244-4-400−2222−22220000-2-2220000−222−2−222−20000000000
χ334-44-400−2i22i22i2−2i200001-11-13−3−33ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ70000000000
χ344-44-400−2i22i22i2−2i200001-11-1−333−3ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ230000000000
χ354-44-400−2i22i22i2−2i20000-22-220000−i2i2i2−i2i2−i2−i2i20000000000
χ364-44-4002i2−2i2−2i22i200001-11-13−3−33−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ70000000000
χ374-44-4002i2−2i2−2i22i200001-11-1−333−3−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ230000000000
χ384-44-4002i2−2i2−2i22i20000-22-220000i2−i2−i2i2−i2i2i2−i20000000000
χ396666-6-6000022-2-200000000000000000000000000
χ406-6-66-6600002-2-2200000000000000000000000000

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