Finite Group Databasebeta

← Group #10714457

Character table — Group #10714457

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112222222222222444444444444488888888888888161616161616161616161616242424242424242448484848
order12222344446881212666888121212242424241616161624244848484848484848444412121212121212122488161616162288
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
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
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
χ1122222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ1222222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ1322222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-11111000000000000
χ1422222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-1000000000000
χ15222-2-222-22-2222222-2-22-2-2-2-2222220000-2-200000000002i−2i00002i2i−2i−2i000000000000
χ16222-2-222-22-2222222-2-22-2-2-2-2222220000-2-20000000000−2i2i0000−2i−2i2i2i000000000000
χ17222-2-222-22-22-2-2222-2-2-222-2-22-2-2-2-20000220000000000000000000000000000002i−2i
χ18222-2-222-22-22-2-2222-2-2-222-2-22-2-2-2-2000022000000000000000000000000000000−2i2i
χ19222-2-22-22-22200-2-22-2-200022-2000022−2−2002222−2−2−2−2000000000000002i−2i−i2−i2i2i20000
χ20222-2-22-22-22200-2-22-2-200022-2000022−2−2002222−2−2−2−200000000000000−2i2ii2i2−i2−i20000
χ21222-2-22-22-22200-2-22-2-200022-20000−2−22200−2−2−2−22222000000000000002i−2ii2i2−i2−i20000
χ22222-2-22-22-22200-2-22-2-200022-20000−2−22200−2−2−2−2222200000000000000−2i2i−i2−i2i2i20000
χ23222-2-2-12-22-2-122-1-1-1112-2-211-1-1-1-1-1000011−i3−i3i3i3−i3−i3i3i3002i−2i33−3−3−i−iii000000000000
χ24222-2-2-12-22-2-122-1-1-1112-2-211-1-1-1-1-1000011−i3−i3i3i3−i3−i3i3i300−2i2i−3−333ii−i−i000000000000
χ25222-2-2-12-22-2-122-1-1-1112-2-211-1-1-1-1-1000011i3i3−i3−i3i3i3−i3−i3002i−2i−3−333−i−iii000000000000
χ26222-2-2-12-22-2-122-1-1-1112-2-211-1-1-1-1-1000011i3i3−i3−i3i3i3−i3−i300−2i2i33−3−3ii−i−i000000000000
χ2722-22-2222-2-220022-22-20002-2-20000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i20000000000002-200−i2i2−i2i20000
χ2822-22-2222-2-220022-22-20002-2-20000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2000000000000-2200i2−i2i2−i20000
χ2922-22-2222-2-220022-22-20002-2-20000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i20000000000002-200i2−i2i2−i20000
χ3022-22-2222-2-220022-22-20002-2-20000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2000000000000-2200−i2i2−i2i20000
χ3122-22-22-2-222222-2-2-22-2-22-2-222-2-22200002-200000000000000000000000000002-200
χ3222-22-22-2-222222-2-2-22-2-22-2-222-2-22200002-20000000000000000000000000000-2200
χ3322-22-22-2-2222-2-2-2-2-22-22-22-22222-2-20000-22000000002-2002-22-20000000000000000
χ3422-22-22-2-2222-2-2-2-2-22-22-22-22222-2-20000-2200000000-2200-22-220000000000000000
χ3522-22-2-1-2-222-1-2-2111-112-221-1-1-1-11100001-13−3−33−333−32-200-11-113−33−3000000000000
χ3622-22-2-1-2-222-1-2-2111-112-221-1-1-1-11100001-13−3−33−333−3-22001-11-1−33−33000000000000
χ3722-22-2-1-2-222-1-2-2111-112-221-1-1-1-11100001-1−333−33−3−332-200-11-11−33−33000000000000
χ3822-22-2-1-2-222-1-2-2111-112-221-1-1-1-11100001-1−333−33−3−33-22001-11-13−33−3000000000000
χ3922-2-222-222-2222-2-2-2-22-2-222-22-2-2220000-220000000000000000000000002-2-220000
χ4022-2-222-222-2222-2-2-2-22-2-222-22-2-2220000-22000000000000000000000000-222-20000
χ4122-2-222-222-22-2-2-2-2-2-2222-22-2222-2-22i−2i−2i2i2-22i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ4222-2-222-222-22-2-2-2-2-2-2222-22-2222-2-2−2i2i2i−2i2-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ4322-2-22-1-222-2-1-2-21111-122-2-11-1-1-1112i−2i−2i2i-11−ii−iii−ii−i00003−3−33i3−i3−i3i3000000000000
χ4422-2-22-1-222-2-1-2-21111-122-2-11-1-1-1112i−2i−2i2i-11−ii−iii−ii−i0000−333−3−i3i3i3−i3000000000000
χ4522-2-22-1-222-2-1-2-21111-122-2-11-1-1-111−2i2i2i−2i-11i−ii−i−ii−ii00003−3−33−i3i3i3−i3000000000000
χ4622-2-22-1-222-2-1-2-21111-122-2-11-1-1-111−2i2i2i−2i-11i−ii−i−ii−ii0000−333−3i3−i3−i3i3000000000000
χ47444444-4-4-4-4400-4-4444000-4-4-4000000000000000000000000000000000000000000
χ4844444-24444-2-4-4-2-2-2-2-2-4-4-4-2-2-2222200002200000000000000000000000000000000
χ4944444-2-4-4-4-4-20022-2-2-20002220000000000i6i6−i6−i6−i6−i6i6i6000000000000000000000000
χ5044444-2-4-4-4-4-20022-2-2-20002220000000000−i6−i6i6i6i6i6−i6−i6000000000000000000000000
χ51444-4-4-24-44-4-2-4-4-2-2-222-44422-222220000-2-200000000000000000000000000000000
χ52444-4-4-2-44-44-20022-222000-2-2200002222−22−2200−2−2−2−22222000000000000000000000000
χ53444-4-4-2-44-44-20022-222000-2-220000−22−222222002222−2−2−2−2000000000000000000000000
χ5444-44-4-244-4-4-200-2-22-22000-2220000−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ5544-44-4-244-4-4-200-2-22-22000-22200002i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ5644-44-4-2-4-444-244222-22-44-42-2-222-2-20000-2200000000000000000000000000000000
χ5744-4-4444-4-4440044-4-44000-44-4000000000000000000000000000000000000000000
χ5844-4-44-24-4-44-200-2-222-20002-2200000000006−6−666−6−66000000000000000000000000
χ5944-4-44-24-4-44-200-2-222-20002-220000000000−666−6−666−6000000000000000000000000
χ6044-4-44-2-444-4-2442222-2-4-44-22-222-2-200002-200000000000000000000000000000000
χ618-800080000-842−42000000000000042−4200000000000000000000000000000000000000
χ628-800080000-8−42420000000000000−424200000000000000000000000000000000000000
χ638-8000-40000442−4243−4300000000026−26−222200000000000000000000000000000000000000
χ648-8000-40000442−42−4343000000000−2626−222200000000000000000000000000000000000000
χ658-8000-400004−424243−43000000000−262622−2200000000000000000000000000000000000000
χ668-8000-400004−4242−434300000000026−2622−2200000000000000000000000000000000000000

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