Finite Group Databasebeta

← Group #10698298

Character table — Group #10698298

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order12222234444444466644661212121212121212888812122424242424242424444444444444121212121212121288884488
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
χ92222222222-2-2-2-22222-2-2222222-2-2-2-20000-2-2000000002222-2-2-2-200000000000000000000
χ102222222222-2-2-2-22222-2-2222222-2-2-2-20000-2-200000000-2-2-2-2222200000000000000000000
χ112222222-2-2-222-2-2-22222-222-2-2-2-2-2-22200002-20000000000000000002-2000022-2-200000000
χ122222222-2-2-222-2-2-22222-222-2-2-2-2-2-22200002-2000000000000000000-220000-2-22200000000
χ132222222-2-2-2-2-222-2222-2222-2-2-2-222-2-20000-22000000000000000000000000000000002-200
χ142222222-2-2-2-2-222-2222-2222-2-2-2-222-2-20000-2200000000000000000000000000000000-2200
χ15222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ16222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ17222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-2-2-1-1-1-1111100000000
χ18222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-2221111-1-1-1-100000000
χ19222222-1-2-2-222-2-2-2-1-1-12-2-1-1111111-1-10000-11−i3−i3−i3−i3i3i3i3i300000000002-2−i3−i3i3i3-1-11100000000
χ20222222-1-2-2-222-2-2-2-1-1-12-2-1-1111111-1-10000-11−i3−i3−i3−i3i3i3i3i30000000000-22i3i3−i3−i311-1-100000000
χ21222222-1-2-2-222-2-2-2-1-1-12-2-1-1111111-1-10000-11i3i3i3i3−i3−i3−i3−i300000000002-2i3i3−i3−i3-1-11100000000
χ22222222-1-2-2-222-2-2-2-1-1-12-2-1-1111111-1-10000-11i3i3i3i3−i3−i3−i3−i30000000000-22−i3−i3i3i311-1-100000000
χ232222-2-2222-22222-2222-2-2-2-222-2-222220000-2-200000000000000000000000000000000002i−2i
χ242222-2-2222-22222-2222-2-2-2-222-2-222220000-2-20000000000000000000000000000000000−2i2i
χ252222-2-2222-2-2-2-2-2-222222-2-222-2-2-2-2-2-200002200000000000000002-2002-22-2000000000000
χ262222-2-2222-2-2-2-2-2-222222-2-222-2-2-2-2-2-20000220000000000000000-2200-22-22000000000000
χ272222-2-22-2-2222-2-22222-22-2-2-2-222-2-2220000-2200000000000000000000000000002i2i−2i−2i0000
χ282222-2-22-2-2222-2-22222-22-2-2-2-222-2-2220000-220000000000000000000000000000−2i−2i2i2i0000
χ292222-2-22-2-22-2-22222222-2-2-2-2-22222-2-22i2i−2i−2i2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ302222-2-22-2-22-2-22222222-2-2-2-2-22222-2-2−2i−2i2i2i2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ312222-2-2-122-2-2-2-2-2-2-1-1-12211-1-11111110000-1-133−3−3−3−333000000002-200-11-113−33−300000000
χ322222-2-2-122-2-2-2-2-2-2-1-1-12211-1-11111110000-1-133−3−3−3−33300000000-22001-11-1−33−3300000000
χ332222-2-2-122-2-2-2-2-2-2-1-1-12211-1-11111110000-1-1−3−33333−3−3000000002-200-11-11−33−3300000000
χ342222-2-2-122-2-2-2-2-2-2-1-1-12211-1-11111110000-1-1−3−33333−3−300000000-22001-11-13−33−300000000
χ352222-2-2-1-2-22-2-2222-1-1-12-21111-1-1-1-1112i2i−2i−2i-11−i−iii−i−iii000000000000−i3i3i3−i33−3−3300000000
χ362222-2-2-1-2-22-2-2222-1-1-12-21111-1-1-1-1112i2i−2i−2i-11−i−iii−i−iii000000000000i3−i3−i3i3−333−300000000
χ372222-2-2-1-2-22-2-2222-1-1-12-21111-1-1-1-111−2i−2i2i2i-11ii−i−iii−i−i000000000000−i3i3i3−i3−333−300000000
χ382222-2-2-1-2-22-2-2222-1-1-12-21111-1-1-1-111−2i−2i2i2i-11ii−i−iii−i−i000000000000i3−i3−i3i33−3−3300000000
χ3922-2-22-222-2-2000022-2-200-222-22-20000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i200002i2i−2i−2i0000000000002−22−20000
χ4022-2-22-222-2-2000022-2-200-222-22-20000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i20000−2i−2i2i2i000000000000−22−220000
χ4122-2-22-222-2-2000022-2-200-222-22-20000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i200002i2i−2i−2i000000000000−22−220000
χ4222-2-22-222-2-2000022-2-200-222-22-20000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i20000−2i−2i2i2i0000000000002−22−20000
χ4322-2-2-222-22-2000022-2-2002-2-222-200002−2−22002−2−222−2−222i2i−2i−2i0000000000000000−i2i2i2−i20000
χ4422-2-2-222-22-2000022-2-2002-2-222-200002−2−22002−2−222−2−22−2i−2i2i2i0000000000000000i2−i2−i2i20000
χ4522-2-2-222-22-2000022-2-2002-2-222-20000−222−200−222−2−222−22i2i−2i−2i0000000000000000i2−i2−i2i20000
χ4622-2-2-222-22-2000022-2-2002-2-222-20000−222−200−222−2−222−2−2i−2i2i2i0000000000000000−i2i2i2−i20000
χ47444444-2444-4-4-4-44-2-2-2-4-4-2-2-2-2-2-22222000022000000000000000000000000000000000000
χ48444444-2-4-4-4-4-444-4-2-2-2-44-2-22222-2-22200002-2000000000000000000000000000000000000
χ494444-4-4-244-44444-4-2-2-2-4-422-2-222-2-2-2-2000022000000000000000000000000000000000000
χ504444-4-4-2-4-4444-4-44-2-2-2-442222-2-222-2-200002-2000000000000000000000000000000000000
χ5144-4-44-44-4440000-44-4-400-44-44-440000000000000000000000000000000000000000000000
χ5244-4-44-4-24-4-400004-222002-2-22-220000−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i20000000000000000000000000000
χ5344-4-44-4-24-4-400004-222002-2-22-2200002i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i20000000000000000000000000000
χ5444-4-44-4-2-4440000-4-222002-22-22-200000000006−66−6−66−660000000000000000000000000000
χ5544-4-44-4-2-4440000-4-222002-22-22-20000000000−66−666−66−60000000000000000000000000000
χ5644-4-4-4444-440000-44-4-4004-44-4-440000000000000000000000000000000000000000000000
χ5744-4-4-44-24-440000-4-22200-22-222-20000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ5844-4-4-44-24-440000-4-22200-22-222-20000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ5944-4-4-44-2-44-400004-22200-222-2-22000022−22−222200−222−2−222−20000000000000000000000000000
χ6044-4-4-44-2-44-400004-22200-222-2-220000−222222−22002−2−222−2−220000000000000000000000000000
χ614-44-4004000004i−4i0-44-4000000004i−4i00000000000000002-22-22i−2i2i−2i00000000000000000000
χ624-44-4004000004i−4i0-44-4000000004i−4i0000000000000000-22-22−2i2i−2i2i00000000000000000000
χ634-44-400400000−4i4i0-44-400000000−4i4i00000000000000002-22-2−2i2i−2i2i00000000000000000000
χ644-44-400400000−4i4i0-44-400000000−4i4i0000000000000000-22-222i−2i2i−2i00000000000000000000
χ654-4-440040004i−4i000-4-4400000000004i−4i000000000000002i−2i−2i2i-222-200000000000000000000
χ664-4-440040004i−4i000-4-4400000000004i−4i00000000000000−2i2i2i−2i2-2-2200000000000000000000
χ674-4-44004000−4i4i000-4-440000000000−4i4i000000000000002i−2i−2i2i2-2-2200000000000000000000
χ684-4-44004000−4i4i000-4-440000000000−4i4i00000000000000−2i2i2i−2i-222-200000000000000000000
χ698-88-800-4000008i−8i04-4400000000−4i4i00000000000000000000000000000000000000000000
χ708-88-800-400000−8i8i04-44000000004i−4i00000000000000000000000000000000000000000000
χ718-8-8800-40008i−8i00044-40000000000−4i4i000000000000000000000000000000000000000000
χ728-8-8800-4000−8i8i00044-400000000004i−4i000000000000000000000000000000000000000000

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