Finite Group Databasebeta

← Group #10714498

Character table — Group #10714498

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112222222222222444444444444488888888888888161616161616161616161616242424242424242448484848
order12222344446881212666888121212242424241616161624244848484848484848448812121212242424242488161616162288
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
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ922222222222-2-222222-2-2-2222-2-2-2-20000-2-20000000000000000000022-2-200000000
χ1022222222222-2-222222-2-2-2222-2-2-2-20000-2-200000000000000000000-2-22200000000
χ11222222-2-2-2-2200-2-2222000-2-2-20000−i2−i2i2i200−i2−i2−i2−i2i2i2i2i2000000000000002i−2i22−2−20000
χ12222222-2-2-2-2200-2-2222000-2-2-20000−i2−i2i2i200−i2−i2−i2−i2i2i2i2i200000000000000−2i2i−2−2220000
χ13222222-2-2-2-2200-2-2222000-2-2-20000i2i2−i2−i200i2i2i2i2−i2−i2−i2−i2000000000000002i−2i−2−2220000
χ14222222-2-2-2-2200-2-2222000-2-2-20000i2i2−i2−i200i2i2i2i2−i2−i2−i2−i200000000000000−2i2i22−2−20000
χ1522222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ1622222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ1722222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-11111000000000000
χ1822222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-1000000000000
χ19222-2-2222-2-2200222-2-2000-2-220000−i2i2−i2i200−i2−i2i2i2−i2−i2i2i20000000000002-200−i2i2−i2i20000
χ20222-2-2222-2-2200222-2-2000-2-220000−i2i2−i2i200−i2−i2i2i2−i2−i2i2i2000000000000-2200i2−i2i2−i20000
χ21222-2-2222-2-2200222-2-2000-2-220000i2−i2i2−i200i2i2−i2−i2i2i2−i2−i20000000000002-200i2−i2i2−i20000
χ22222-2-2222-2-2200222-2-2000-2-220000i2−i2i2−i200i2i2−i2−i2i2i2−i2−i2000000000000-2200−i2i2−i2i20000
χ23222-2-22-2-222222-2-22-2-22-2-222-222-2-200002-20000000000000000000000002i−2i−2i2i0000
χ24222-2-22-2-222222-2-22-2-22-2-222-222-2-200002-2000000000000000000000000−2i2i2i−2i0000
χ25222-2-22-2-2222-2-2-2-22-2-2-22222-2-2-2222-2-22-2222-2-2-2-222000000000000000000000000
χ26222-2-22-2-2222-2-2-2-22-2-2-22222-2-2-222-222-2-22-2-22222-2-2000000000000000000000000
χ27222-2-2-1-2-222-1-2-211-111-222-1-1111-1-12-2-221-1-1-11111-1-1000033−3−333−3−3000000000000
χ28222-2-2-1-2-222-1-2-211-111-222-1-1111-1-12-2-221-1-1-11111-1-10000−3−333−3−333000000000000
χ29222-2-2-1-2-222-1-2-211-111-222-1-1111-1-1-222-21-111-1-1-1-111000033−3−3−3−333000000000000
χ30222-2-2-1-2-222-1-2-211-111-222-1-1111-1-1-222-21-111-1-1-1-1110000−3−33333−3−3000000000000
χ3122-22-222-22-222222-22-2-22-2-22-222220000-2-2000000002i−2i002i−2i2i−2i0000000000000000
χ3222-22-222-22-222222-22-2-22-2-22-222220000-2-200000000−2i2i00−2i2i−2i2i0000000000000000
χ3322-22-222-22-22-2-222-22-22-22-22-2-2-2-2-20000220000000000000000000000000000002i−2i
χ3422-22-222-22-22-2-222-22-22-22-22-2-2-2-2-2000022000000000000000000000000000000−2i2i
χ3522-22-2-12-22-2-122-1-11-11-22-21-11-1-1-1-1000011−i3i3−i3i3−i3i3−i3i32i−2i00−ii−ii3−33−3000000000000
χ3622-22-2-12-22-2-122-1-11-11-22-21-11-1-1-1-1000011−i3i3−i3i3−i3i3−i3i3−2i2i00i−ii−i−33−33000000000000
χ3722-22-2-12-22-2-122-1-11-11-22-21-11-1-1-1-1000011i3−i3i3−i3i3−i3i3−i32i−2i00−ii−ii−33−33000000000000
χ3822-22-2-12-22-2-122-1-11-11-22-21-11-1-1-1-1000011i3−i3i3−i3i3−i3i3−i3−2i2i00i−ii−i3−33−3000000000000
χ3922-2-222-222-2222-2-2-2-22-2-22-22222-2-20000-2200000000000000000000000000002-200
χ4022-2-222-222-2222-2-2-2-22-2-22-22222-2-20000-220000000000000000000000000000-2200
χ4122-2-222-222-22-2-2-2-2-2-2222-2-222-2-22200002-200000000002-200002-2-22000000000000
χ4222-2-222-222-22-2-2-2-2-2-2222-2-222-2-22200002-20000000000-220000-222-2000000000000
χ4322-2-22-1-222-2-1-2-21111-122-21-1-111-1-10000-11−i3i3i3−i3i3−i3−i3i3002-2−i3i3i3−i3-111-1000000000000
χ4422-2-22-1-222-2-1-2-21111-122-21-1-111-1-10000-11−i3i3i3−i3i3−i3−i3i300-22i3−i3−i3i31-1-11000000000000
χ4522-2-22-1-222-2-1-2-21111-122-21-1-111-1-10000-11i3−i3−i3i3−i3i3i3−i3002-2i3−i3−i3i3-111-1000000000000
χ4622-2-22-1-222-2-1-2-21111-122-21-1-111-1-10000-11i3−i3−i3i3−i3i3i3−i300-22−i3i3i3−i31-1-11000000000000
χ4744444-24444-2-4-4-2-2-2-2-2-4-4-4-2-2-2222200002200000000000000000000000000000000
χ4844444-2-4-4-4-4-20022-2-2-20002220000−2i2−2i22i22i200i2i2i2i2−i2−i2−i2−i2000000000000000000000000
χ4944444-2-4-4-4-4-20022-2-2-200022200002i22i2−2i2−2i200−i2−i2−i2−i2i2i2i2i2000000000000000000000000
χ50444-4-4-244-4-4-200-2-2-22200022-20000−2i22i2−2i22i200i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ51444-4-4-244-4-4-200-2-2-22200022-200002i2−2i22i2−2i200−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ52444-4-4-2-4-444-24422-2224-4-4-2-22-2-2220000-2200000000000000000000000000000000
χ5344-44-44-44-44400-4-4-44-40004-44000000000000000000000000000000000000000000
χ5444-44-4-24-44-4-2-4-4-2-22-224-442-2222220000-2-200000000000000000000000000000000
χ5544-44-4-2-44-44-200222-22000-22-200000000006−66−6−66−66000000000000000000000000
χ5644-44-4-2-44-44-200222-22000-22-20000000000−66−666−66−6000000000000000000000000
χ5744-4-4444-4-4440044-4-440004-4-4000000000000000000000000000000000000000000
χ5844-4-44-24-4-44-200-2-222-2000-22200000000006−6−666−6−66000000000000000000000000
χ5944-4-44-24-4-44-200-2-222-2000-2220000000000−666−6−666−6000000000000000000000000
χ6044-4-44-2-444-4-2442222-2-4-442-2-2-2-22200002-200000000000000000000000000000000
χ618-800080000-842−420000000000042−420000000000000000000000000000000000000000
χ628-800080000-8−424200000000000−42420000000000000000000000000000000000000000
χ638-8000-40000442−4243−43000000000−222226−2600000000000000000000000000000000000000
χ648-8000-40000442−42−4343000000000−2222−262600000000000000000000000000000000000000
χ658-8000-400004−424243−4300000000022−22−262600000000000000000000000000000000000000
χ668-8000-400004−4242−434300000000022−2226−2600000000000000000000000000000000000000

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