Finite Group Databasebeta

← Group #10714481

Character table — Group #10714481

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112222222222222444444444444488888888888888161616161616161616161616242424242424242448484848
order122223444468812126668881212122424242416161616242448484848484848482444661212121212122488161616164488
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
χ15222-2-222-22-2222222-2-22-2-2-2-2222220000-2-20000000000000000000000000000002i−2i
χ16222-2-222-22-2222222-2-22-2-2-2-2222220000-2-2000000000000000000000000000000−2i2i
χ17222-2-222-22-22-2-2222-2-2-222-2-22-2-2-2-200002200000000002i−2i00002i2i−2i−2i000000000000
χ18222-2-222-22-22-2-2222-2-2-222-2-22-2-2-2-20000220000000000−2i2i0000−2i−2i2i2i000000000000
χ19222-2-22-22-22200-2-22-2-200022-20000−i2−i2i2i200−i2−i2−i2−i2i2i2i2i2000000000000002i−2i22−2−20000
χ20222-2-22-22-22200-2-22-2-200022-20000−i2−i2i2i200−i2−i2−i2−i2i2i2i2i200000000000000−2i2i−2−2220000
χ21222-2-22-22-22200-2-22-2-200022-20000i2i2−i2−i200i2i2i2i2−i2−i2−i2−i2000000000000002i−2i−2−2220000
χ22222-2-22-22-22200-2-22-2-200022-20000i2i2−i2−i200i2i2i2i2−i2−i2−i2−i200000000000000−2i2i22−2−20000
χ23222-2-2-12-22-2-1-2-2-1-1-111-22211-111110000-1-133−3−333−3−3002i−2i−i3i3−i3i3−i−iii000000000000
χ24222-2-2-12-22-2-1-2-2-1-1-111-22211-111110000-1-133−3−333−3−300−2i2ii3−i3i3−i3ii−i−i000000000000
χ25222-2-2-12-22-2-1-2-2-1-1-111-22211-111110000-1-1−3−333−3−333002i−2ii3−i3i3−i3−i−iii000000000000
χ26222-2-2-12-22-2-1-2-2-1-1-111-22211-111110000-1-1−3−333−3−33300−2i2i−i3i3−i3i3ii−i−i000000000000
χ2722-22-22-222-2222-2-2-2-22-2-222-22-2-2222-22-22-22-22-22-22-2000000000000000000000000
χ2822-22-22-222-2222-2-2-2-22-2-222-22-2-222-22-222-2-22-22-22-22000000000000000000000000
χ2922-22-22-222-22-2-2-2-2-2-2222-22-2222-2-20000-220000000000000000000000002i−2i2i−2i0000
χ3022-22-22-222-22-2-2-2-2-2-2222-22-2222-2-20000-22000000000000000000000000−2i2i−2i2i0000
χ3122-22-2-1-222-2-1221111-1-2-22-11-111-1-12-22-2-11-11-11-11-110000−i3i3i3−i3−i3i3−i3i3000000000000
χ3222-22-2-1-222-2-1221111-1-2-22-11-111-1-12-22-2-11-11-11-11-110000i3−i3−i3i3i3−i3i3−i3000000000000
χ3322-22-2-1-222-2-1221111-1-2-22-11-111-1-1-22-22-111-11-11-11-10000−i3i3i3−i3i3−i3i3−i3000000000000
χ3422-22-2-1-222-2-1221111-1-2-22-11-111-1-1-22-22-111-11-11-11-10000i3−i3−i3i3−i3i3−i3i3000000000000
χ3522-2-22222-2-220022-22-20002-2-20000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i20000000000002-200−i2i2i2−i20000
χ3622-2-22222-2-220022-22-20002-2-20000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i2000000000000-2200i2−i2−i2i20000
χ3722-2-22222-2-220022-22-20002-2-20000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i20000000000002-200i2−i2−i2i20000
χ3822-2-22222-2-220022-22-20002-2-20000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i2000000000000-2200−i2i2i2−i20000
χ3922-2-222-2-222222-2-2-22-2-22-2-222-2-2220000-2200000000000000000000000000002-200
χ4022-2-222-2-222222-2-2-22-2-22-2-222-2-2220000-220000000000000000000000000000-2200
χ4122-2-222-2-2222-2-2-2-2-22-22-22-22222-2-200002-2000000002-20022-2-20000000000000000
χ4222-2-222-2-2222-2-2-2-2-22-22-22-22222-2-200002-200000000-2200-2-2220000000000000000
χ4322-2-22-1-2-222-1-2-2111-112-221-1-1-1-1110000-113−3−333−3−332-200-1-1113−3−33000000000000
χ4422-2-22-1-2-222-1-2-2111-112-221-1-1-1-1110000-113−3−333−3−33-220011-1-1−333−3000000000000
χ4522-2-22-1-2-222-1-2-2111-112-221-1-1-1-1110000-11−333−3−333−32-200-1-111−333−3000000000000
χ4622-2-22-1-2-222-1-2-2111-112-221-1-1-1-1110000-11−333−3−333−3-220011-1-13−3−33000000000000
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
χ51444-4-4-24-44-4-244-2-2-2224-4-422-2-2-2-2-200002200000000000000000000000000000000
χ52444-4-4-2-44-44-20022-222000-2-220000−2i2−2i22i22i200i2i2i2i2−i2−i2−i2−i2000000000000000000000000
χ53444-4-4-2-44-44-20022-222000-2-2200002i22i2−2i2−2i200−i2−i2−i2−i2i2i2i2i2000000000000000000000000
χ5444-44-444-4-4440044-4-44000-44-4000000000000000000000000000000000000000000
χ5544-44-4-24-4-44-200-2-222-20002-220000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ5644-44-4-24-4-44-200-2-222-20002-220000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ5744-44-4-2-444-4-2-4-42222-244-4-22-2-2-22200002-200000000000000000000000000000000
χ5844-4-44-244-4-4-200-2-22-22000-2220000−2i22i22i2−2i200i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ5944-4-44-244-4-4-200-2-22-22000-22200002i2−2i2−2i22i200−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ6044-4-44-2-4-444-244222-22-44-42-2-222-2-200002-200000000000000000000000000000000
χ618-800080000-8−4i24i20000000000000−4i24i200000000000000000000000000000000000000
χ628-800080000-84i2−4i200000000000004i2−4i200000000000000000000000000000000000000
χ638-8000-400004−4i24i243−430000000002i6−2i62i2−2i200000000000000000000000000000000000000
χ648-8000-400004−4i24i2−4343000000000−2i62i62i2−2i200000000000000000000000000000000000000
χ658-8000-4000044i2−4i243−43000000000−2i62i6−2i22i200000000000000000000000000000000000000
χ668-8000-4000044i2−4i2−43430000000002i6−2i6−2i22i200000000000000000000000000000000000000

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