Finite Group Databasebeta

← Group #10695930

Character table — Group #10695930

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order122222344444466644466121212121212121288881212242424242424242424446612121212121222444444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-1-1-1-1-111
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1111111-1-1
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ92222222222-2-22222-2-2-222-2-22222-2-20000-2-2000000000000000000002200-2-200000000
χ102222222222-2-22222-2-2-222-2-22222-2-20000-2-200000000000000000000-2-2002200000000
χ112222222-2-2-222-2222-22-222-2-2-2-2-2-22200002-200000000002-2000022-2-200000000000000
χ122222222-2-2-222-2222-22-222-2-2-2-2-2-22200002-20000000000-220000-2-22200000000000000
χ132222222-2-2-2-2-2-22222-222222-2-2-2-2-2-20000-2200000000000000000000002200-2-2000000
χ142222222-2-2-2-2-2-22222-222222-2-2-2-2-2-20000-220000000000000000000000-2-20022000000
χ15222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ16222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ17222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-1111100000000000000
χ18222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-100000000000000
χ19222222-1-2-2-222-2-1-1-1-22-2-1-1111111-1-10000-11−i3−i3−i3−i3i3i3i3i3002-2−i3i3−i3i3-1-11100000000000000
χ20222222-1-2-2-222-2-1-1-1-22-2-1-1111111-1-10000-11−i3−i3−i3−i3i3i3i3i300-22i3−i3i3−i311-1-100000000000000
χ21222222-1-2-2-222-2-1-1-1-22-2-1-1111111-1-10000-11i3i3i3i3−i3−i3−i3−i3002-2i3−i3i3−i3-1-11100000000000000
χ22222222-1-2-2-222-2-1-1-1-22-2-1-1111111-1-10000-11i3i3i3i3−i3−i3−i3−i300-22−i3i3−i3i311-1-100000000000000
χ232222-2-2222-222-2222-2-22-2-2-2-222-2-2220000-22000000000000000000000000000022-2-200
χ242222-2-2222-222-2222-2-22-2-2-2-222-2-2220000-220000000000000000000000000000-2-22200
χ252222-2-2222-2-2-2-222222-2-2-22222-2-2-2-22i2i−2i−2i2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ262222-2-2222-2-2-2-222222-2-2-22222-2-2-2-2−2i−2i2i2i2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ272222-2-22-2-222222222-2-2-2-222-2-222220000-2-2000000000000000000000000000000002-2
χ282222-2-22-2-222222222-2-2-2-222-2-222220000-2-200000000000000000000000000000000-22
χ292222-2-22-2-22-2-22222-222-2-2-2-2-2-222-2-2000022000000002-20022-2-2000000000000000000
χ302222-2-22-2-22-2-22222-222-2-2-2-2-2-222-2-200002200000000-2200-2-222000000000000000000
χ312222-2-2-122-2-2-2-2-1-1-122-211-1-1-1-111112i2i−2i−2i-11−i−iii−i−iii0000−i3i3i3−i33−33−300000000000000
χ322222-2-2-122-2-2-2-2-1-1-122-211-1-1-1-111112i2i−2i−2i-11−i−iii−i−iii0000i3−i3−i3i3−33−3300000000000000
χ332222-2-2-122-2-2-2-2-1-1-122-211-1-1-1-11111−2i−2i2i2i-11ii−i−iii−i−i0000−i3i3i3−i3−33−3300000000000000
χ342222-2-2-122-2-2-2-2-1-1-122-211-1-1-1-11111−2i−2i2i2i-11ii−i−iii−i−i0000i3−i3−i3i33−33−300000000000000
χ352222-2-2-1-2-22-2-22-1-1-1-222111111-1-1110000-1-133−3−3−3−3332-200-1-1113−3−3300000000000000
χ362222-2-2-1-2-22-2-22-1-1-1-222111111-1-1110000-1-133−3−3−3−333-220011-1-1−333−300000000000000
χ372222-2-2-1-2-22-2-22-1-1-1-222111111-1-1110000-1-1−3−33333−3−32-200-1-111−333−300000000000000
χ382222-2-2-1-2-22-2-22-1-1-1-222111111-1-1110000-1-1−3−33333−3−3-220011-1-13−3−3300000000000000
χ3922-2-22-222-2-2002-2-220002-2002-22-200−i2i2−i2i200−i2i2−i2i2−i2i2−i2i20000000000002-2000000−i2i2−i2i200
χ4022-2-22-222-2-2002-2-220002-2002-22-200−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2000000000000-22000000i2−i2i2−i200
χ4122-2-22-222-2-2002-2-220002-2002-22-200i2−i2i2−i200i2−i2i2−i2i2−i2i2−i20000000000002-2000000i2−i2i2−i200
χ4222-2-22-222-2-2002-2-220002-2002-22-200i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2000000000000-22000000−i2i2−i2i200
χ4322-2-2-2222-2200-2-2-22000-22002-2-22002−2−22002−2−222−2−2200000000000000002i−2i00−i2i2i2−i200
χ4422-2-2-2222-2200-2-2-22000-22002-2-22002−2−22002−2−222−2−220000000000000000−2i2i00i2−i2−i2i200
χ4522-2-2-2222-2200-2-2-22000-22002-2-2200−222−200−222−2−222−200000000000000002i−2i00i2−i2−i2i200
χ4622-2-2-2222-2200-2-2-22000-22002-2-2200−222−200−222−2−222−20000000000000000−2i2i00−i2i2i2−i200
χ47444444-2444-4-44-2-2-2-4-4-4-2-222-2-2-2-2220000220000000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-2-2-24-44-2-2-2-222222200002-20000000000000000000000000000000000
χ494444-4-4-244-444-4-2-2-2-4-442222-2-222-2-200002-20000000000000000000000000000000000
χ504444-4-4-2-4-44444-2-2-24-4-422-2-222-2-2-2-20000220000000000000000000000000000000000
χ5144-4-44-44-44400-4-4-440004-400-44-44000000000000000000000000000000000000000000
χ5244-4-44-4-24-4-400422-2000-2200-22-2200−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ5344-4-44-4-24-4-400422-2000-2200-22-22002i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ5444-4-44-4-2-44400-422-2000-22002-22-2000000006−66−6−66−6600000000000000000000000000
χ5544-4-44-4-2-44400-422-2000-22002-22-200000000−66−666−66−600000000000000000000000000
χ5644-4-4-444-44-4004-4-44000-4400-444-4000000000000000000000000000000000000000000
χ5744-4-4-44-24-4400-422-20002-200-222-20022−22−222200−222−2−222−200000000000000000000000000
χ5844-4-4-44-24-4400-422-20002-200-222-200−222222−22002−2−222−2−2200000000000000000000000000
χ5944-4-4-44-2-44-400422-20002-2002-2-2200000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ6044-4-4-44-2-44-400422-20002-2002-2-2200000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ614-44-40040004i−4i04-4-4000000000004i−4i00000000000000000000000000002-2002i−2i000000
χ624-44-40040004i−4i04-4-4000000000004i−4i0000000000000000000000000000-2200−2i2i000000
χ634-44-4004000−4i4i04-4-400000000000−4i4i00000000000000000000000000002-200−2i2i000000
χ644-44-4004000−4i4i04-4-400000000000−4i4i0000000000000000000000000000-22002i−2i000000
χ658-88-800-40008i−8i0-44400000000000−4i4i0000000000000000000000000000000000000000
χ668-88-800-4000−8i8i0-444000000000004i−4i0000000000000000000000000000000000000000
χ678-8-88008000000-88-800000000000000000000000000000000000000000000000000000
χ688-8-8800-40000004-440000043−430000000000000000000000000000000000000000000000
χ698-8-8800-40000004-4400000−43430000000000000000000000000000000000000000000000

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