Finite Group Databasebeta

← Group #10698914

Character table — Group #10698914

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order12222234444444466644661212121212121212444412121212121212121212888888888888242424242424242488884488
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
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1
χ9222222222-2-2-22-22222-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ10222222222-2-2-22-22222-2-222-2-2-2-22222-2-222-2-2-2-2-2-222220000000000000000000000000000
χ112222222-2-2222-22-2222-2-2222222-2-2-2-20000-2-200000000000000002i−2i002i2i−2i−2i000000000000
χ122222222-2-2222-22-2222-2-2222222-2-2-2-20000-2-20000000000000000−2i2i00−2i−2i2i2i000000000000
χ132222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-20000220000000000000000002i−2i00002i2i−2i−2i00000000
χ142222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2000022000000000000000000−2i2i0000−2i−2i2i2i00000000
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
χ19222222-122-2-2-22-22-1-1-1-2-2-1-11111-1-1-1-122-2-211-1-1-1-11111000000000000−i3i3−i3i3−i3i3−i3i300000000
χ20222222-122-2-2-22-22-1-1-1-2-2-1-11111-1-1-1-122-2-211-1-1-1-11111000000000000i3−i3i3−i3i3−i3i3−i300000000
χ21222222-122-2-2-22-22-1-1-1-2-2-1-11111-1-1-1-1-2-222111111-1-1-1-1000000000000−i3i3−i3i3i3−i3i3−i300000000
χ22222222-122-2-2-22-22-1-1-1-2-2-1-11111-1-1-1-1-2-222111111-1-1-1-1000000000000i3−i3i3−i3−i3i3−i3i300000000
χ23222222-1-2-2222-22-2-1-1-1-2-2-1-1-1-1-1-11111000011−i3−i3i3i3−i3−i3i3i3000000002i−2i00−i−iii3−3−3300000000
χ24222222-1-2-2222-22-2-1-1-1-2-2-1-1-1-1-1-11111000011−i3−i3i3i3−i3−i3i3i300000000−2i2i00ii−i−i−333−300000000
χ25222222-1-2-2222-22-2-1-1-1-2-2-1-1-1-1-1-11111000011i3i3−i3−i3i3i3−i3−i3000000002i−2i00−i−iii−333−300000000
χ26222222-1-2-2222-22-2-1-1-1-2-2-1-1-1-1-1-11111000011i3i3−i3−i3i3i3−i3−i300000000−2i2i00ii−i−i3−3−3300000000
χ27222222-1-2-2-2-2-2-2-2-2-1-1-122-1-1111111110000-1-1−i3−i3i3i3i3i3−i3−i300000000002i−2i3−3−33−i−iii00000000
χ28222222-1-2-2-2-2-2-2-2-2-1-1-122-1-1111111110000-1-1−i3−i3i3i3i3i3−i3−i30000000000−2i2i−333−3ii−i−i00000000
χ29222222-1-2-2-2-2-2-2-2-2-1-1-122-1-1111111110000-1-1i3i3−i3−i3−i3−i3i3i300000000002i−2i−333−3−i−iii00000000
χ30222222-1-2-2-2-2-2-2-2-2-1-1-122-1-1111111110000-1-1i3i3−i3−i3−i3−i3i3i30000000000−2i2i3−3−33ii−i−i00000000
χ312222-2-222-222-22-2-22222-2-2-222-2-22-22-200002-200000000000000000000000000002i2i−2i−2i0000
χ322222-2-222-222-22-2-22222-2-2-222-2-22-22-200002-20000000000000000000000000000−2i−2i2i2i0000
χ332222-2-222-2-2-2222-2222-22-2-2-2-2222-22-20000-22000000002222-2-2-2-200000000000000000000
χ342222-2-222-2-2-2222-2222-22-2-2-2-2222-22-20000-2200000000-2-2-2-2222200000000000000000000
χ352222-2-22-2222-2-2-22222-22-2-222-2-2-22-220000-2200000000000000000000000000000000002-2
χ362222-2-22-2222-2-2-22222-22-2-222-2-2-22-220000-220000000000000000000000000000000000-22
χ372222-2-22-22-2-22-2222222-2-2-2-2-222-22-2200002-2000000000000000000000000000000002-200
χ382222-2-22-22-2-22-2222222-2-2-2-2-222-22-2200002-200000000000000000000000000000000-2200
χ3922-2-22-2222000-20-2-22-2002-2000022-2-22-200002-22-2000022−2−222−2−20000000000002−22−20000
χ4022-2-22-2222000-20-2-22-2002-2000022-2-22-200002-22-20000−2−222−2−222000000000000−22−220000
χ4122-2-22-2222000-20-2-22-2002-2000022-2-2-220000-22-22000022−2−222−2−2000000000000−22−220000
χ4222-2-22-2222000-20-2-22-2002-2000022-2-2-220000-22-220000−2−222−2−2220000000000002−22−20000
χ4322-2-2-2222-2000-202-22-200-2200002-2-22002i−2i0000002i−2i2i−2i22−2−2−2−222000000000000−i2i2i2−i20000
χ4422-2-2-2222-2000-202-22-200-2200002-2-22002i−2i0000002i−2i2i−2i−2−22222−2−2000000000000i2−i2−i2i20000
χ4522-2-2-2222-2000-202-22-200-2200002-2-2200−2i2i000000−2i2i−2i2i22−2−2−2−222000000000000i2−i2−i2i20000
χ4622-2-2-2222-2000-202-22-200-2200002-2-2200−2i2i000000−2i2i−2i2i−2−22222−2−2000000000000−i2i2i2−i20000
χ474444-4-4-24-444-44-4-4-2-2-24-422-2-222-22-220000-22000000000000000000000000000000000000
χ484444-4-4-24-4-4-4444-4-2-2-2-442222-2-2-22-2200002-2000000000000000000000000000000000000
χ494444-4-4-2-4444-4-4-44-2-2-2-4422-2-2222-22-200002-2000000000000000000000000000000000000
χ504444-4-4-2-44-4-44-444-2-2-24-42222-2-22-22-20000-22000000000000000000000000000000000000
χ5144-4-44-44-4-4000404-44-4004-40000-4-444000000000000000000000000000000000000000000
χ5244-4-44-4-244000-40-42-2200-220000-2-2224-40000-22-2200000000000000000000000000000000
χ5344-4-44-4-244000-40-42-2200-220000-2-222-4400002-22-200000000000000000000000000000000
χ5444-4-44-4-2-4-40004042-2200-22000022-2-2000000−2i32i32i3−2i300000000000000000000000000000000
χ5544-4-44-4-2-4-40004042-2200-22000022-2-20000002i3−2i3−2i32i300000000000000000000000000000000
χ5644-4-4-444-4400040-4-44-400-440000-444-4000000000000000000000000000000000000000000
χ5744-4-4-44-24-4000-4042-22002-20000-222-2004i−4i000000−2i2i−2i2i0000000000000000000000000000
χ5844-4-4-44-24-4000-4042-22002-20000-222-200−4i4i0000002i−2i2i−2i0000000000000000000000000000
χ5944-4-4-44-2-4400040-42-22002-200002-2-22000000000023−23−23230000000000000000000000000000
χ6044-4-4-44-2-4400040-42-22002-200002-2-220000000000−232323−230000000000000000000000000000
χ614-44-4004000040-404-4-40000004-4000000000000000000000022−2222−2200000000000000000000
χ624-44-4004000040-404-4-40000004-40000000000000000000000−2222−222200000000000000000000
χ634-44-40040000-40404-4-4000000-44000000000000000000−2i22i2−2i22i2000000000000000000000000
χ644-44-40040000-40404-4-4000000-440000000000000000002i2−2i22i2−2i2000000000000000000000000
χ654-4-44004004i−4i0000-4-4400004i−4i000000000000000000002i−2i−2i2i2-2-2200000000000000000000
χ664-4-44004004i−4i0000-4-4400004i−4i00000000000000000000−2i2i2i−2i-222-200000000000000000000
χ674-4-4400400−4i4i0000-4-440000−4i4i000000000000000000002i−2i−2i2i-222-200000000000000000000
χ684-4-4400400−4i4i0000-4-440000−4i4i00000000000000000000−2i2i2i−2i2-2-2200000000000000000000
χ698-88-800-4000080-80-444000000-440000000000000000000000000000000000000000000000
χ708-88-800-40000-8080-4440000004-40000000000000000000000000000000000000000000000
χ718-8-8800-4008i−8i000044-40000−4i4i000000000000000000000000000000000000000000000000
χ728-8-8800-400−8i8i000044-400004i−4i000000000000000000000000000000000000000000000000

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