Finite Group Databasebeta

← Group #10698823

Character table — Group #10698823

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12222234444446664446612121212121212124444121212121212121212128888242424242424242488888888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1
χ92222222222-2-22222-2-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000
χ102222222222-2-22222-2-2-222-2-2-2-22222-2-222-2-2-2-2-2-2222200000000000000000000000000
χ112222222-2-2-222-2222-22-2222222-2-2-2-20000-2-2000000002i−2i002i2i−2i−2i000000000000000000
χ122222222-2-2-222-2222-22-2222222-2-2-2-20000-2-200000000−2i2i00−2i−2i2i2i000000000000000000
χ132222222-2-2-2-2-2-22222-2222-2-2-2-2-2-2-2-200002200000000002i−2i00002i2i−2i−2i00000000000000
χ142222222-2-2-2-2-2-22222-2222-2-2-2-2-2-2-2-20000220000000000−2i2i0000−2i−2i2i2i00000000000000
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
χ19222222-1222-2-22-1-1-1-2-2-2-1-11111-1-1-1-122-2-211-1-1-1-111110000−i3i3−i3i3−i3i3−i3i300000000000000
χ20222222-1222-2-22-1-1-1-2-2-2-1-11111-1-1-1-122-2-211-1-1-1-111110000i3−i3i3−i3i3−i3i3−i300000000000000
χ21222222-1222-2-22-1-1-1-2-2-2-1-11111-1-1-1-1-2-222111111-1-1-1-10000−i3i3−i3i3i3−i3i3−i300000000000000
χ22222222-1222-2-22-1-1-1-2-2-2-1-11111-1-1-1-1-2-222111111-1-1-1-10000i3−i3i3−i3−i3i3−i3i300000000000000
χ23222222-1-2-2-222-2-1-1-1-22-2-1-1-1-1-1-11111000011−i3−i3i3i3−i3−i3i3i32i−2i00−i−iii3−3−3300000000000000
χ24222222-1-2-2-222-2-1-1-1-22-2-1-1-1-1-1-11111000011−i3−i3i3i3−i3−i3i3i3−2i2i00ii−i−i−333−300000000000000
χ25222222-1-2-2-222-2-1-1-1-22-2-1-1-1-1-1-11111000011i3i3−i3−i3i3i3−i3−i32i−2i00−i−iii−333−300000000000000
χ26222222-1-2-2-222-2-1-1-1-22-2-1-1-1-1-1-11111000011i3i3−i3−i3i3i3−i3−i3−2i2i00ii−i−i3−3−3300000000000000
χ27222222-1-2-2-2-2-2-2-1-1-12-22-1-1111111110000-1-1−i3−i3i3i3i3i3−i3−i3002i−2i3−3−33−i−iii00000000000000
χ28222222-1-2-2-2-2-2-2-1-1-12-22-1-1111111110000-1-1−i3−i3i3i3i3i3−i3−i300−2i2i−333−3ii−i−i00000000000000
χ29222222-1-2-2-2-2-2-2-1-1-12-22-1-1111111110000-1-1i3i3−i3−i3−i3−i3i3i3002i−2i−333−3−i−iii00000000000000
χ30222222-1-2-2-2-2-2-2-1-1-12-22-1-1111111110000-1-1i3i3−i3−i3−i3−i3i3i300−2i2i3−3−33ii−i−i00000000000000
χ312222-2-2222-222-2222-2-22-2-222-2-22-22-200002-20000000000000000000022-2-20000000000
χ322222-2-2222-222-2222-2-22-2-222-2-22-22-200002-200000000000000000000-2-2220000000000
χ332222-2-2222-2-2-2-222222-2-2-2-2-2222-22-20000-2200000000000000000000000000002i2i−2i−2i00
χ342222-2-2222-2-2-2-222222-2-2-2-2-2222-22-20000-220000000000000000000000000000−2i−2i2i2i00
χ352222-2-22-2-222222222-2-2-2-222-2-2-22-220000-2200000000000000000000000022-2-2000000
χ362222-2-22-2-222222222-2-2-2-222-2-2-22-220000-22000000000000000000000000-2-222000000
χ372222-2-22-2-22-2-22222-222-2-2-2-222-22-2200002-2000000000000000000000000000000002-2
χ382222-2-22-2-22-2-22222-222-2-2-2-222-22-2200002-200000000000000000000000000000000-22
χ3922-2-22-22-22200-2-22-20002-20000-2-222002-20000002-22-2000000000000−i2i2−i2i20000−i2i2−i2i200
χ4022-2-22-22-22200-2-22-20002-20000-2-222002-20000002-22-2000000000000i2−i2i2−i20000i2−i2i2−i200
χ4122-2-22-22-22200-2-22-20002-20000-2-22200-22000000-22-22000000000000−i2i2−i2i20000i2−i2i2−i200
χ4222-2-22-22-22200-2-22-20002-20000-2-22200-22000000-22-22000000000000i2−i2i2−i20000−i2i2−i2i200
χ4322-2-2-222-22-2002-22-2000-220000-222-22i−2i00002i−2i2i−2i0000000000000000−i2i2i2−i200002−2−2200
χ4422-2-2-222-22-2002-22-2000-220000-222-22i−2i00002i−2i2i−2i0000000000000000i2−i2−i2i20000−222−200
χ4522-2-2-222-22-2002-22-2000-220000-222-2−2i2i0000−2i2i−2i2i0000000000000000−i2i2i2−i20000−222−200
χ4622-2-2-222-22-2002-22-2000-220000-222-2−2i2i0000−2i2i−2i2i0000000000000000i2−i2−i2i200002−2−2200
χ474444-4-4-244-444-4-2-2-2-4-4422-2-222-22-220000-220000000000000000000000000000000000
χ484444-4-4-244-4-4-4-4-2-2-244-42222-2-2-22-2200002-20000000000000000000000000000000000
χ494444-4-4-2-4-44444-2-2-24-4-422-2-2222-22-200002-20000000000000000000000000000000000
χ504444-4-4-2-4-44-4-44-2-2-2-4442222-2-22-22-20000-220000000000000000000000000000000000
χ5144-4-44-444-4-4004-44-40004-4000044-4-40000000000000000000000000000000000000000
χ5244-4-44-4-24-4-40042-22000-220000-2-2220000000000−2i32i32i3−2i300000000000000000000000000
χ5344-4-44-4-24-4-40042-22000-220000-2-22200000000002i3−2i3−2i32i300000000000000000000000000
χ5444-4-44-4-2-44400-42-22000-22000022-2-2004-4000000-22-2200000000000000000000000000
χ5544-4-44-4-2-44400-42-22000-22000022-2-200-440000002-22-200000000000000000000000000
χ5644-4-4-4444-4400-4-44-4000-4400004-4-440000000000000000000000000000000000000000
χ5744-4-4-44-24-4400-42-220002-20000-222-200000023−23−2323000000000000000000000000000000
χ5844-4-4-44-24-4400-42-220002-20000-222-2000000−232323−23000000000000000000000000000000
χ5944-4-4-44-2-44-40042-220002-200002-2-224i−4i0000−2i2i−2i2i000000000000000000000000000000
χ6044-4-4-44-2-44-40042-220002-200002-2-22−4i4i00002i−2i2i−2i000000000000000000000000000000
χ614-4-440040004-404-4-4000004-400000000000000000000000000000000000000−2i22i2000000
χ624-4-440040004-404-4-4000004-4000000000000000000000000000000000000002i2−2i2000000
χ634-4-44004000-4404-4-400000-44000000000000000000000000000000000000−2i22i200000000
χ644-4-44004000-4404-4-400000-440000000000000000000000000000000000002i2−2i200000000
χ658-88-8008000000-8-8800000000000000000000000000000000000000000000000000000
χ668-88-800-400000044-4000000043−4300000000000000000000000000000000000000000000
χ678-88-800-400000044-40000000−434300000000000000000000000000000000000000000000
χ688-8-8800-40008-80-44400000-440000000000000000000000000000000000000000000000
χ698-8-8800-4000-880-444000004-40000000000000000000000000000000000000000000000

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