Finite Group Databasebeta

← Group #10698073

Character table — Group #10698073

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order1222222222344446664466666612121212888812122424242424242424444444444444121212121212121288884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-111-1-1
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111
χ922222222222-2-2-2-2222-2-2222222-2-2-2-20000-2-2000000002222-2-2-2-200000000000000000000
χ1022222222222-2-2-2-2222-2-2222222-2-2-2-20000-2-200000000-2-2-2-2222200000000000000000000
χ112222222222-12222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ122222222222-12222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ132222222222-12222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-2-2-1-1-1-1111100000000
χ142222222222-12222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-2221111-1-1-1-100000000
χ15222222-2-2-2-222222222-2-222-2-2-2-222220000-2-2000000000000000000000000000022-2-20000
χ16222222-2-2-2-222222222-2-222-2-2-2-222220000-2-20000000000000000000000000000-2-2220000
χ17222222-2-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-22i2i−2i−2i222i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ18222222-2-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-2−2i−2i2i2i22−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000
χ19222222-2-2-2-2-1-2-2-2-2-1-1-122-1-1111111112i2i−2i−2i-1-1−i−i−i−iiiii000000000000−i3i3−i3i333−3−300000000
χ20222222-2-2-2-2-1-2-2-2-2-1-1-122-1-1111111112i2i−2i−2i-1-1−i−i−i−iiiii000000000000i3−i3i3−i3−3−33300000000
χ21222222-2-2-2-2-1-2-2-2-2-1-1-122-1-111111111−2i−2i2i2i-1-1iiii−i−i−i−i000000000000−i3i3−i3i3−3−33300000000
χ22222222-2-2-2-2-1-2-2-2-2-1-1-122-1-111111111−2i−2i2i2i-1-1iiii−i−i−i−i000000000000i3−i3i3−i333−3−300000000
χ232222-2-22-22-2222-2-22222-2-2-22-2-22-2-22200002-20000000000000000002-200002-22-200000000
χ242222-2-22-22-2222-2-22222-2-2-22-2-22-2-22200002-2000000000000000000-220000-22-2200000000
χ252222-2-22-22-22-2-222222-22-2-22-2-2222-2-20000-22000000000000000000000000000000002-200
χ262222-2-22-22-22-2-222222-22-2-22-2-2222-2-20000-2200000000000000000000000000000000-2200
χ272222-2-22-22-2-122-2-2-1-1-12-211-111-111-1-10000-11−i3−i3i3i3−i3−i3i3i300000000002-2−i3i3i3−i3-11-1100000000
χ282222-2-22-22-2-122-2-2-1-1-12-211-111-111-1-10000-11−i3−i3i3i3−i3−i3i3i30000000000-22i3−i3−i3i31-11-100000000
χ292222-2-22-22-2-122-2-2-1-1-12-211-111-111-1-10000-11i3i3−i3−i3i3i3−i3−i300000000002-2i3−i3−i3i3-11-1100000000
χ302222-2-22-22-2-122-2-2-1-1-12-211-111-111-1-10000-11i3i3−i3−i3i3i3−i3−i30000000000-22−i3i3i3−i31-11-100000000
χ312222-2-2-22-22222-2-2222-22-2-2-222-2-2-2220000-2200000000000000000000000000000000002-2
χ322222-2-2-22-22222-2-2222-22-2-2-222-2-2-2220000-220000000000000000000000000000000000-22
χ332222-2-2-22-222-2-2222222-2-2-2-222-222-2-200002-200000000000000002-200-2-222000000000000
χ342222-2-2-22-222-2-2222222-2-2-2-222-222-2-200002-20000000000000000-220022-2-2000000000000
χ352222-2-2-22-22-1-2-222-1-1-12-2111-1-11-1-1110000-1133−3−3−3−333000000002-20011-1-1−333−300000000
χ362222-2-2-22-22-1-2-222-1-1-12-2111-1-11-1-1110000-1133−3−3−3−33300000000-2200-1-1113−3−3300000000
χ372222-2-2-22-22-1-2-222-1-1-12-2111-1-11-1-1110000-11−3−33333−3−3000000002-20011-1-13−3−3300000000
χ382222-2-2-22-22-1-2-222-1-1-12-2111-1-11-1-1110000-11−3−33333−3−300000000-2200-1-111−333−300000000
χ3922-2-22-222-2-2200002-2-2002-222-2-200002−22−2002−22−22−22−222-2-200000000000000002−22−20000
χ4022-2-22-222-2-2200002-2-2002-222-2-200002−22−2002−22−22−22−2-2-2220000000000000000−22−220000
χ4122-2-22-222-2-2200002-2-2002-222-2-20000−22−2200−22−22−22−2222-2-20000000000000000−22−220000
χ4222-2-22-222-2-2200002-2-2002-222-2-20000−22−2200−22−22−22−22-2-22200000000000000002−22−20000
χ4322-2-22-2-2-222200002-2-2002-2-2-2220000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i200002i2i−2i−2i0000000000002−2−220000
χ4422-2-22-2-2-222200002-2-2002-2-2-2220000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i20000−2i−2i2i2i000000000000−222−20000
χ4522-2-22-2-2-222200002-2-2002-2-2-2220000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i200002i2i−2i−2i000000000000−222−20000
χ4622-2-22-2-2-222200002-2-2002-2-2-2220000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i20000−2i−2i2i2i0000000000002−2−220000
χ474444444444-2-4-4-4-4-2-2-2-4-4-2-2-2-2-2-22222000022000000000000000000000000000000000000
χ48444444-4-4-4-4-24444-2-2-2-4-4-2-22222-2-2-2-2000022000000000000000000000000000000000000
χ494444-4-44-44-4-2-4-444-2-2-2-4422-222-2-2-22200002-2000000000000000000000000000000000000
χ504444-4-4-44-44-244-4-4-2-2-2-44222-2-2222-2-200002-2000000000000000000000000000000000000
χ5144-4-44-444-4-4-20000-22200-22-2-222000022−2222−2200−22−22−22−220000000000000000000000000000
χ5244-4-44-444-4-4-20000-22200-22-2-2220000−2222−2222002−22−22−22−20000000000000000000000000000
χ5344-4-44-4-4-444-20000-22200-2222-2-20000−2i22i22i2−2i200i2−i2i2−i2−i2i2−i2i20000000000000000000000000000
χ5444-4-44-4-4-444-20000-22200-2222-2-200002i2−2i2−2i22i200−i2i2−i2i2i2−i2i2−i20000000000000000000000000000
χ5544-4-4-444-4-44400004-4-400-444-44-40000000000000000000000000000000000000000000000
χ5644-4-4-444-4-44-20000-222002-2-22-220000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ5744-4-4-444-4-44-20000-222002-2-22-220000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ5844-4-4-44-444-4400004-4-400-44-44-440000000000000000000000000000000000000000000000
χ5944-4-4-44-444-4-20000-222002-22-22-200000000006−6−66−666−60000000000000000000000000000
χ6044-4-4-44-444-4-20000-222002-22-22-20000000000−666−66−6−660000000000000000000000000000
χ614-44-40000004004-4-4-44000000004-400000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ624-44-40000004004-4-4-44000000004-40000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ634-44-4000000400-44-4-4400000000-4400000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ644-44-4000000400-44-4-4400000000-440000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ654-4-4400000044i−4i00-44-400000000004i−4i000000000000002i−2i−2i2i-222-200000000000000000000
χ664-4-4400000044i−4i00-44-400000000004i−4i00000000000000−2i2i2i−2i2-2-2200000000000000000000
χ674-4-440000004−4i4i00-44-40000000000−4i4i000000000000002i−2i−2i2i2-2-2200000000000000000000
χ684-4-440000004−4i4i00-44-40000000000−4i4i00000000000000−2i2i2i−2i-222-200000000000000000000
χ698-88-8000000-4008-844-400000000-4400000000000000000000000000000000000000000000
χ708-88-8000000-400-8844-4000000004-400000000000000000000000000000000000000000000
χ718-8-88000000-48i−8i004-440000000000−4i4i000000000000000000000000000000000000000000
χ728-8-88000000-4−8i8i004-4400000000004i−4i000000000000000000000000000000000000000000

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