Finite Group Databasebeta

← Group #10714493

Character table — Group #10714493

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112222222222222444444444444488888888888888161616161616161616161616242424242424242448484848
order1222234444666886688812121212242424242466881212242424242424226666882424242416161616161616164488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ92222222222222-2-222-2-2-22222-2-2-2-22222-2-222-2-2-2-2-2-2000000000000000000000000
χ102222222222222-2-222-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000000000
χ11222222-2-2-2-22220022000-2-2-2-2000000002i−2i00002i2i−2i−2i00000000000022−2−2−i2−i2i2i20000
χ12222222-2-2-2-22220022000-2-2-2-2000000002i−2i00002i2i−2i−2i000000000000−2−222i2i2−i2−i20000
χ13222222-2-2-2-22220022000-2-2-2-200000000−2i2i0000−2i−2i2i2i00000000000022−2−2i2i2−i2−i20000
χ14222222-2-2-2-22220022000-2-2-2-200000000−2i2i0000−2i−2i2i2i000000000000−2−222−i2−i2i2i20000
χ1522222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1000000000000
χ1622222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-21111-2-21111000000000000
χ1722222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-1-2-211-2-211-1-1111122-1-1-1-1-2-21111000000000000
χ1822222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-1-2-211-2-211-1-11111-2-2111122-1-1-1-1000000000000
χ1922222-12222-1-1-1-2-2-1-1-2-2-2-1-1-1-1111122-1-1-2-2-1-111111100−i3−i3i3i300−i3−i3i3i3000000000000
χ2022222-12222-1-1-1-2-2-1-1-2-2-2-1-1-1-1111122-1-1-2-2-1-111111100i3i3−i3−i300i3i3−i3−i3000000000000
χ2122222-12222-1-1-1-2-2-1-1-2-2-2-1-1-1-11111-2-211221111-1-1-1-100−i3−i3i3i300i3i3−i3−i3000000000000
χ2222222-12222-1-1-1-2-2-1-1-2-2-2-1-1-1-11111-2-211221111-1-1-1-100i3i3−i3−i300−i3−i3i3i3000000000000
χ23222-2-2222-2-222200-2-20002-22-200002-22200-2-2000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ24222-2-2222-2-222200-2-20002-22-200002-22200-2-2000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ25222-2-2222-2-222200-2-20002-22-20000-22-2-20022000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ26222-2-2222-2-222200-2-20002-22-20000-22-2-20022000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ27222-2-22-2-22222222-2-22-2-2-22-22222200000000-2-200000000000000002i−2i−2i2i00000000
χ28222-2-22-2-22222222-2-22-2-2-22-22222200000000-2-20000000000000000−2i2i2i−2i00000000
χ29222-2-22-2-222222-2-2-2-2-222-22-22-2-2-2-20000000022000000000000000000002-2-220000
χ30222-2-22-2-222222-2-2-2-2-222-22-22-2-2-2-2000000002200000000000000000000-222-20000
χ3122-22-222-22-2-2-22222-2-22-22-2-2222-2-2000000002-20000000000000000000000002i−2i00
χ3222-22-222-22-2-2-22222-2-22-22-2-2222-2-2000000002-2000000000000000000000000−2i2i00
χ3322-22-222-22-2-2-22-2-22-22-222-2-22-2-22200000000-22000000000000000000000000002i−2i
χ3422-22-222-22-2-2-22-2-22-22-222-2-22-2-22200000000-2200000000000000000000000000−2i2i
χ3522-2-222-222-2-2-2222-22-2-22-2-22222-2-200000000-2200002-22-22-2000000000000000000
χ3622-2-222-222-2-2-2222-22-2-22-2-22222-2-200000000-220000-22-22-22000000000000000000
χ3722-2-222-222-2-2-22-2-2-2222-2-2-222-2-222000000002-200000000002-22-22-2000000000000
χ3822-2-222-222-2-2-22-2-2-2222-2-2-222-2-222000000002-20000000000-22-22-22000000000000
χ3922-2-22-1-222-211-1221-1-2-2211-1-1-1-11100−i3i300−i3i31-1−i3i3−i3i32-2-11-1100−i3i3i3−i3000000000000
χ4022-2-22-1-222-211-1221-1-2-2211-1-1-1-11100−i3i300−i3i31-1−i3i3−i3i3-221-11-100i3−i3−i3i3000000000000
χ4122-2-22-1-222-211-1221-1-2-2211-1-1-1-11100i3−i300i3−i31-1i3−i3i3−i32-2-11-1100i3−i3−i3i3000000000000
χ4222-2-22-1-222-211-1221-1-2-2211-1-1-1-11100i3−i300i3−i31-1i3−i3i3−i3-221-11-100−i3i3i3−i3000000000000
χ4322-2-22-1-222-211-1-2-21-122-211-1-111-1-100−i3i300−i3i3-11i3−i3i3−i300−i3i3i3−i32-2-11-11000000000000
χ4422-2-22-1-222-211-1-2-21-122-211-1-111-1-100−i3i300−i3i3-11i3−i3i3−i300i3−i3−i3i3-221-11-1000000000000
χ4522-2-22-1-222-211-1-2-21-122-211-1-111-1-100i3−i300i3−i3-11−i3i3−i3i300−i3i3i3−i3-221-11-1000000000000
χ4622-2-22-1-222-211-1-2-21-122-211-1-111-1-100i3−i300i3−i3-11−i3i3−i3i300i3−i3−i3i32-2-11-11000000000000
χ4744444-2-4-4-4-4-2-2-200-2-20002222000000004i−4i0000−2i−2i2i2i000000000000000000000000
χ4844444-2-4-4-4-4-2-2-200-2-2000222200000000−4i4i00002i2i−2i−2i000000000000000000000000
χ49444-4-4-244-4-4-2-2-20022000-22-2200004-4-2-20022000000000000000000000000000000
χ50444-4-4-244-4-4-2-2-20022000-22-220000-442200-2-2000000000000000000000000000000
χ51444-4-4-2-4-444-2-2-244224-4-42-22-2-2-2-2-200000000220000000000000000000000000000
χ52444-4-4-2-4-444-2-2-2-4-422-4442-22-2222200000000-2-20000000000000000000000000000
χ5344-44-44-44-44-4-44004-4000-444-4000000000000000000000000000000000000000000
χ5444-44-4-24-44-422-244-22-44-4-222-2-2-22200000000-220000000000000000000000000000
χ5544-44-4-24-44-422-2-4-4-224-44-222-222-2-2000000002-20000000000000000000000000000
χ5644-44-4-2-44-4422-200-220002-2-22000000−2i32i3002i3−2i3000000000000000000000000000000
χ5744-44-4-2-44-4422-200-220002-2-220000002i3−2i300−2i32i3000000000000000000000000000000
χ5844-4-4444-4-44-4-4400-4400044-4-4000000000000000000000000000000000000000000
χ5944-4-44-24-4-4422-2002-2000-2-2220000000000000023−23−2323000000000000000000000000
χ6044-4-44-24-4-4422-2002-2000-2-22200000000000000−232323−23000000000000000000000000
χ618-80008000000-842−4200000000042−420000000000000000000000000000000000000000
χ628-80008000000-8−4242000000000−42420000000000000000000000000000000000000000
χ638-8000-40000−4i34i3442−42000000000−22222i6−2i600000000000000000000000000000000000000
χ648-8000-40000−4i34i34−424200000000022−22−2i62i600000000000000000000000000000000000000
χ658-8000-400004i3−4i3442−42000000000−2222−2i62i600000000000000000000000000000000000000
χ668-8000-400004i3−4i34−424200000000022−222i6−2i600000000000000000000000000000000000000

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