Finite Group Databasebeta

← Group #72343111

Character table — Group #72343111

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1122222224444444444444488888888888161616161616323232323232323232323232323232323232323232323232
order1224488882444444444888824888881616161616161616161624448888888888883232323232323232
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111-1-111-1-11111111-1-11-1-1-1-11111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ61111111111-1-111-1-11111111-1-11-1-1-1-11111-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ71111111111-1-111-1-11111111-1-11-1-1-1-11111-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ81111111111-1-111-1-11111111-1-11-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ911111-1-111111-1-1-1-11-1-1-1-1-111-1111-1-1-1-1-1-11111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111-1-111111-1-1-1-11-1-1-1-1-111-1111-1-1-1-1-1-11111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111-1-111111-1-1-1-11-1-1-1-1-111-1111-1-1-1-1-1-11111-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211111-1-111111-1-1-1-11-1-1-1-1-111-1111-1-1-1-1-1-11111-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311111-1-1111-1-1-1-1111-1-1-1-1-11-111-1-111-1-1-1-1-1-1111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411111-1-1111-1-1-1-1111-1-1-1-1-11-111-1-111-1-1-1-1-1-1111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511111-1-1111-1-1-1-1111-1-1-1-1-11-111-1-111-1-1-1-1-1-11111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111-1-1111-1-1-1-1111-1-1-1-1-11-111-1-111-1-1-1-1-1-11111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ182222222222-2-222-2-22222222-2-22-2-2-2-2-2-2-2-222-2-222000000000000000000000000
χ19222222222-2002200-2-2-22-2-2200-2000022-2-2002-2000000000000002i−2i2i−2i00000000
χ20222222222-2002200-2-2-22-2-2200-2000022-2-2002-200000000000000−2i2i−2i2i00000000
χ21222222222-2002200-2-2-22-2-2200-20000-2-22200-2200000000002i−2i2i−2i000000000000
χ22222222222-2002200-2-2-22-2-2200-20000-2-22200-220000000000−2i2i−2i2i000000000000
χ232222222-2-2222-2-2-2-22-2-2222-22-2-2-2-22200000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ242222222-2-2222-2-2-2-22-2-2222-22-2-2-2-22200000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ252222222-2-22-2-2-2-2222-2-2222-2-22-222-2-200000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ262222222-2-22-2-2-2-2222-2-2222-2-22-222-2-200000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ2722222-2-222222-2-2-2-22-2-2-2-2-222-2222-2-22222-2-2-2-222000000000000000000000000
χ2822222-2-2222-2-2-2-2222-2-2-2-2-22-222-2-222222222-2-2-2-2000000000000000000000000
χ2922222-2-222-200-2-200-222-222200-2000022-2-200-2200000000002-2-22000000000000
χ3022222-2-222-200-2-200-222-222200-2000022-2-200-220000000000-222-2000000000000
χ3122222-2-222-200-2-200-222-222200-20000-2-222002-2000000000000002-2-2200000000
χ3222222-2-222-200-2-200-222-222200-20000-2-222002-200000000000000-222-200000000
χ3322222-2-2-2-22222222222-2-2-2-222-2-2-2-2-2000000000000000000000000002−2−222−2−22
χ3422222-2-2-2-22222222222-2-2-2-222-2-2-2-2-200000000000000000000000000−222−2−222−2
χ3522222-2-2-2-22-2-222-2-2222-2-2-2-2-2-2-22222000000000000000000000000002−2−22−222−2
χ3622222-2-2-2-22-2-222-2-2222-2-2-2-2-2-2-2222200000000000000000000000000−222−22−2−22
χ374444444-4-4-400-4-400-4444-4-4-400400000000000000000000000000000000000000
χ3844444-4-4-4-4-4004400-4-4-4-444-400400000000000000000000000000000000000000
χ39444-4-400004440000-4000000-40000002i2−2i22i2−2i200002i2−2i2000000000000000000000000
χ40444-4-400004440000-4000000-4000000−2i22i2−2i22i20000−2i22i2000000000000000000000000
χ41444-4-400004-4-40000-400000040000002i2−2i22i2−2i20000−2i22i2000000000000000000000000
χ42444-4-400004-4-40000-40000004000000−2i22i2−2i22i200002i2−2i2000000000000000000000000
χ43444-4-40000-400004440000000-4000002i2−2i2−2i22i22i2−2i20000000000000000000000000000
χ44444-4-40000-400004440000000-400000−2i22i22i2−2i2−2i22i20000000000000000000000000000
χ45444-4-40000-40000-4-4400000004000002i2−2i2−2i22i2−2i22i20000000000000000000000000000
χ46444-4-40000-40000-4-440000000400000−2i22i22i2−2i22i2−2i20000000000000000000000000000
χ4744-44-40044000000004i−4i04i−4i-400000000000000000002-2002i−2i0000000000000000
χ4844-44-40044000000004i−4i04i−4i-40000000000000000000-2200−2i2i0000000000000000
χ4944-44-4004400000000−4i4i0−4i4i-400000000000000000002-200−2i2i0000000000000000
χ5044-44-4004400000000−4i4i0−4i4i-40000000000000000000-22002i−2i0000000000000000
χ5144-44-400-4-4000000004i−4i0−4i4i4000000000000000002-2002i−2i000000000000000000
χ5244-44-400-4-4000000004i−4i0−4i4i400000000000000000-2200−2i2i000000000000000000
χ5344-44-400-4-400000000−4i4i04i−4i4000000000000000002-200−2i2i000000000000000000
χ5444-44-400-4-400000000−4i4i04i−4i400000000000000000-22002i−2i000000000000000000
χ5588-8-8888000000000000-800000000000000000000000000000000000000000000
χ5688-8-88-8-8000000000000800000000000000000000000000000000000000000000
χ578-800042−424i2−4i204i−4i4i−4i4-4000000000022−222i2−2i20000000000000000000000000000000000
χ588-800042−424i2−4i20−4i4i4i−4i-440000000000−2222−2i22i20000000000000000000000000000000000
χ598-800042−42−4i24i204i−4i−4i4i-440000000000−22222i2−2i20000000000000000000000000000000000
χ608-800042−42−4i24i20−4i4i−4i4i4-4000000000022−22−2i22i20000000000000000000000000000000000
χ618-8000−42424i2−4i204i−4i−4i4i-44000000000022−22−2i22i20000000000000000000000000000000000
χ628-8000−42424i2−4i20−4i4i−4i4i4-40000000000−22222i2−2i20000000000000000000000000000000000
χ638-8000−4242−4i24i204i−4i4i−4i4-40000000000−2222−2i22i20000000000000000000000000000000000
χ648-8000−4242−4i24i20−4i4i4i−4i-44000000000022−222i2−2i20000000000000000000000000000000000

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