Finite Group Databasebeta

← Group #72341292

Character table — Group #72341292

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112266668888121212121212121212121212242424242424242424242424242424242424323232324848484848484848646464646464
order122244224422442244444444442222444444444444443666444488886612121212
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ31111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1
χ41111111111-1-1-1-1111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1
χ51111-1-111-1-111-1-111-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-1111111-1-111-1-111-1-1-1-1
χ61111-1-111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1111111-1-111-1-11111-1-1-1-1
χ71111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-111
χ81111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1111111-1-1-1-111-1-1-1-111
χ911-1-1i−i1-1i−i1-1i−i1-1ii−i−i11-1-11-11-11-1i−ii−i1-1i−ii−i1-1i−i11-1-11-1i−i1-1i−i1-1i−ii−i
χ1011-1-1i−i1-1i−i1-1i−i1-1ii−i−i-1-1111-1-11-11−ii−ii1-1i−i−ii-11−ii11-1-1-11−ii-11−ii1-1i−ii−i
χ1111-1-1i−i1-1i−i-11−ii1-1ii−i−i11-1-11-11-1-11i−i−ii-11−iii−i-11−ii11-1-1-11−ii1-1i−i-11i−i−ii
χ1211-1-1i−i1-1i−i-11−ii1-1ii−i−i-1-1111-1-111-1−iii−i-11−ii−ii1-1i−i11-1-11-1i−i-11−ii-11i−i−ii
χ1311-1-1−ii1-1−ii1-1−ii1-1−i−iii11-1-11-11-11-1−ii−ii1-1−ii−ii1-1−ii11-1-11-1−ii1-1−ii1-1−ii−ii
χ1411-1-1−ii1-1−ii1-1−ii1-1−i−iii-1-1111-1-11-11i−ii−i1-1−iii−i-11i−i11-1-1-11i−i-11i−i1-1−ii−ii
χ1511-1-1−ii1-1−ii-11i−i1-1−i−iii11-1-11-11-1-11−iii−i-11i−i−ii-11i−i11-1-1-11i−i1-1−ii-11−iii−i
χ1611-1-1−ii1-1−ii-11i−i1-1−i−iii-1-1111-1-111-1i−i−ii-11i−ii−i1-1−ii11-1-11-1−ii-11i−i-11−iii−i
χ1722222222222222222222000022000000002222000000-1-1-1-100000000-1-1-1-1-1-1
χ182222222222-2-2-2-222222200002200000000-2-2-2-2000000-1-1-1-10000000011-1-111
χ192222-2-222-2-222-2-222-2-2-2-20000220000000022-2-2000000-1-1-1-100000000-1-11111
χ202222-2-222-2-2-2-22222-2-2-2-200002200000000-2-222000000-1-1-1-1000000001111-1-1
χ2122-2-22i−2i2-22i−2i2-22i−2i2-22i2i−2i−2i00002-2000000002-22i−2i000000-1-11100000000-11−ii−ii
χ2222-2-22i−2i2-22i−2i-22−2i2i2-22i2i−2i−2i00002-200000000-22−2i2i000000-1-111000000001-1−iii−i
χ2322-2-2−2i2i2-2−2i2i2-2−2i2i2-2−2i−2i2i2i00002-2000000002-2−2i2i000000-1-11100000000-11i−ii−i
χ2422-2-2−2i2i2-2−2i2i-222i−2i2-2−2i−2i2i2i00002-200000000-222i−2i000000-1-111000000001-1i−i−ii
χ2533333333333333-1-1-1-1-1-11111-1-111111111-1-1-1-11111110000-1-1-1-1-1-1-1-1000000
χ2633333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000011111111000000
χ273333333333-3-3-3-3-1-1-1-1-1-11111-1-111-1-111-1-1111111-1-1-1-100001111-1-1-1-1000000
χ283333333333-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111110000-1-1-1-11111000000
χ293333-3-333-3-333-3-3-1-111111111-1-11111-1-1-1-1-1-111-1-111-1-10000-1-111-1-111000000
χ303333-3-333-3-333-3-3-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111000011-1-111-1-1000000
χ313333-3-333-3-3-3-333-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-111000011-1-1-1-111000000
χ323333-3-333-3-3-3-333-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-10000-1-11111-1-1000000
χ3333-3-33i−3i3-33i−3i3-33i−3i-11−i−iii11-1-1-111-11-1i−ii−i-11−iii−i1-1i−i0000-11−ii-11−ii000000
χ3433-3-33i−3i3-33i−3i3-33i−3i-11−i−iii-1-111-11-11-11−ii−ii-11−ii−ii-11−ii00001-1i−i1-1i−i000000
χ3533-3-33i−3i3-33i−3i-33−3i3i-11−i−iii11-1-1-111-1-11i−i−ii1-1i−ii−i-11−ii00001-1i−i-11−ii000000
χ3633-3-33i−3i3-33i−3i-33−3i3i-11−i−iii-1-111-11-111-1−iii−i1-1i−i−ii1-1i−i0000-11−ii1-1i−i000000
χ3733-3-3−3i3i3-3−3i3i3-3−3i3i-11ii−i−i11-1-1-111-11-1−ii−ii-11i−i−ii1-1−ii0000-11i−i-11i−i000000
χ3833-3-3−3i3i3-3−3i3i3-3−3i3i-11ii−i−i-1-111-11-11-11i−ii−i-11i−ii−i-11i−i00001-1−ii1-1−ii000000
χ3933-3-3−3i3i3-3−3i3i-333i−3i-11ii−i−i11-1-1-111-1-11−iii−i1-1−ii−ii-11i−i00001-1−ii-11i−i000000
χ4033-3-3−3i3i3-3−3i3i-333i−3i-11ii−i−i-1-111-11-111-1i−i−ii1-1−iii−i1-1−ii0000-11i−i1-1−ii000000
χ41666666-2-2-2-20000222-22-20000-2-200220022000000-2-2-2-2000000000000000000
χ42666666-2-2-2-20000222-22-20000-2-200-2-200-2-20000002222000000000000000000
χ43666666-2-2-2-20000-2-2-22-22222222-2-200-2-2000000220000000000000000000000
χ44666666-2-2-2-20000-2-2-22-22-2-2-2-222220022000000-2-20000000000000000000000
χ456666-6-6-2-222000022-22-220000-2-2002200-2-2000000-2-222000000000000000000
χ466666-6-6-2-222000022-22-220000-2-200-2-2002200000022-2-2000000000000000000
χ476666-6-6-2-2220000-2-22-22-2222222-2-20022000000-2-20000000000000000000000
χ486666-6-6-2-2220000-2-22-22-2-2-2-2-2222200-2-2000000220000000000000000000000
χ4966-6-66i−6i-22−2i2i00002-22i−2i−2i2i0000-22002-2002i−2i000000-22−2i2i000000000000000000
χ5066-6-66i−6i-22−2i2i00002-22i−2i−2i2i0000-2200-2200−2i2i0000002-22i−2i000000000000000000
χ5166-6-66i−6i-22−2i2i0000-22−2i2i2i−2i22-2-22-2-2200−2i2i0000002i−2i0000000000000000000000
χ5266-6-66i−6i-22−2i2i0000-22−2i2i2i−2i-2-2222-22-2002i−2i000000−2i2i0000000000000000000000
χ5366-6-6−6i6i-222i−2i00002-2−2i2i2i−2i0000-22002-200−2i2i000000-222i−2i000000000000000000
χ5466-6-6−6i6i-222i−2i00002-2−2i2i2i−2i0000-2200-22002i−2i0000002-2−2i2i000000000000000000
χ5566-6-6−6i6i-222i−2i0000-222i−2i−2i2i22-2-22-2-22002i−2i000000−2i2i0000000000000000000000
χ5666-6-6−6i6i-222i−2i0000-222i−2i−2i2i-2-2222-22-200−2i2i0000002i−2i0000000000000000000000
χ578-88-800000000000000004-44-4000000000000000000002-22-200000000000000
χ588-88-80000000000000000-44-44000000000000000000002-22-200000000000000
χ598-8-8800000000000000004-4-44000000000000000000002-2-2200000000000000
χ608-8-880000000000000000-444-4000000000000000000002-2-2200000000000000
χ6116-1616-160000000000000000000000000000000000000000-22-2200000000000000
χ6216-16-16160000000000000000000000000000000000000000-222-200000000000000

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