Finite Group Databasebeta

← Group #10782810

Character table — Group #10782810

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121212121212161616161616161616162424242448484848
order12222234444666444466121212121212121224448888121224242424242424248888888824666121212121288884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11-1-1111-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-111-1-1-11111-1-111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1-111-1-111-1-111
χ91111-1-111111111-1-11-1-1-1111-1-1-1-1111-1-111-1-1-111111-1-1-1-111-1-1-1-1-1-11-11111-1-1-1-1-11111-1-11
χ101111-1-111111111-1-11-1-1-1111-1-1-1-1111-1-111-1-1-111111-1-1-1-1-1-11111111-11111-1-1-1-11-1-1-1-111-1
χ111111-1-111111111-1-11-1-1-1111-1-1-1-1111-1-1-1-111-11-1-1-1-1111111-1-1-1-1-1-1-111-1-11-1-111-1111-111-1
χ121111-1-111111111-1-11-1-1-1111-1-1-1-1111-1-1-1-111-11-1-1-1-11111-1-1111111-111-1-11-1-1111-1-1-11-1-11
χ131111-1-111111111-1-11-1-1-1111-1-1-1-11-1-11111-1-1-111111-1-1-1-111-1-11111-11-1-1-1-11111-11-1-1-11-11
χ141111-1-111111111-1-11-1-1-1111-1-1-1-11-1-11111-1-1-111111-1-1-1-1-1-111-1-1-1-1-11-1-1-1-111111-1111-11-1
χ151111-1-111111111-1-11-1-1-1111-1-1-1-11-1-111-1-111-11-1-1-1-1111111-1-111111-1-111-111-1-1-11-1-11-11-1
χ161111-1-111111111-1-11-1-1-1111-1-1-1-11-1-111-1-111-11-1-1-1-11111-1-111-1-1-1-11-1-111-111-1-11-111-11-11
χ1722222222-22-22222-2-2-2222-2-222-2-222-2-220000-2-2000000000000000000200-2-220000000000
χ1822222222-22-22222-2-2-2222-2-222-2-22-222-20000-2-2000000000000000000-20022-20000000000
χ192222222-22-22222-22-2-222-222-2-2-2-2-2000000002-200000000222200000000000000-2-2000000
χ202222222-22-22222-22-2-222-222-2-2-2-2-2000000002-200000000-2-2-2-20000000000000022000000
χ212222222-2-2-2-2222-2-22222-2-2-2-2-222-200000000-220000000000002i2i−2i−2i0000000000002i−2i0000
χ222222222-2-2-2-2222-2-22222-2-2-2-2-222-200000000-22000000000000−2i−2i2i2i000000000000−2i2i0000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-100000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-11111111100000000-2-2-111-1-1-11100000000
χ25222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-100000000-2-21111111100000000
χ26222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111111100000000221-1-1111-1-100000000
χ27222222-12-22-2-1-1-12-2-2-2-1-1-111-1-111-12-2-22000011−i3−i3i3i3−i3−i3i3i30000000000-1−i3i311-1−i3i300000000
χ28222222-12-22-2-1-1-12-2-2-2-1-1-111-1-111-12-2-22000011i3i3−i3−i3i3i3−i3−i30000000000-1i3−i311-1i3−i300000000
χ29222222-12-22-2-1-1-12-2-2-2-1-1-111-1-111-1-222-2000011−i3−i3i3i3−i3−i3i3i300000000001i3−i3-1-11i3−i300000000
χ30222222-12-22-2-1-1-12-2-2-2-1-1-111-1-111-1-222-2000011i3i3−i3−i3i3i3−i3−i300000000001−i3i3-1-11−i3i300000000
χ312222-2-222-22-2222-22-22-2-22-2-2-2-22222-22-200002-2000000000000000000200-22-20000000000
χ322222-2-222-22-2222-22-22-2-22-2-2-2-2222-22-2200002-2000000000000000000-2002-220000000000
χ332222-2-22-22-222222-2-22-2-2-2222222-200000000-2-20000000022-2-2000000000000002-2000000
χ342222-2-22-22-222222-2-22-2-2-2222222-200000000-2-200000000-2-22200000000000000-22000000
χ352222-2-22-2-2-2-2222222-2-2-2-2-2-222-2-2-200000000220000000000002i2i−2i−2i000000000000−2i2i0000
χ362222-2-22-2-2-2-2222222-2-2-2-2-2-222-2-2-20000000022000000000000−2i−2i2i2i0000000000002i−2i0000
χ372222-2-2-12222-1-1-1-2-22-211-1-1-11111-122-2-222-2-21-1-1-1-1-11111000000002-2-1-1-1-1111100000000
χ382222-2-2-12222-1-1-1-2-22-211-1-1-11111-122-2-2-2-2221-11111-1-1-1-100000000-22-111-111-1-100000000
χ392222-2-2-12222-1-1-1-2-22-211-1-1-11111-1-2-22222-2-21-1-1-1-1-1111100000000-221111-1-1-1-100000000
χ402222-2-2-12222-1-1-1-2-22-211-1-1-11111-1-2-222-2-2221-11111-1-1-1-1000000002-21-1-11-1-11100000000
χ412222-2-2-12-22-2-1-1-1-22-2211-11111-1-1-12-22-20000-11−i3−i3i3i3i3i3−i3−i30000000000-1−i3i31-11i3−i300000000
χ422222-2-2-12-22-2-1-1-1-22-2211-11111-1-1-12-22-20000-11i3i3−i3−i3−i3−i3i3i30000000000-1i3−i31-11−i3i300000000
χ432222-2-2-12-22-2-1-1-1-22-2211-11111-1-1-1-22-220000-11−i3−i3i3i3i3i3−i3−i300000000001i3−i3-11-1−i3i300000000
χ442222-2-2-12-22-2-1-1-1-22-2211-11111-1-1-1-22-220000-11i3i3−i3−i3−i3−i3i3i300000000001−i3i3-11-1i3−i300000000
χ45444444-2-44-44-2-2-2-44-4-4-2-22-2-22222200000000-220000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-2-4-444-2-222222-2-22000000002-20000000000000000000000000000000000
χ474444-4-4-2-44-44-2-2-24-4-44222-2-2-2-2-2-2200000000220000000000000000000000000000000000
χ484444-4-4-2-4-4-4-4-2-2-2444-422222-2-222200000000-2-20000000000000000000000000000000000
χ4944-4-4004040-44-4-400000004-400000000022−22000022−2222−22000000000000000000000000000000
χ5044-4-4004040-44-4-400000004-4000000000−22220000−2222−2222000000000000000000000000000000
χ5144-4-40040-4044-4-40000000-4400000000000−2i22i2000000−2i22i2−2i22i200000000000000000000000000
χ5244-4-40040-4044-4-40000000-44000000000002i2−2i20000002i2−2i22i2−2i200000000000000000000000000
χ5344-4-400-2040-4-2220000000-2223−2323−230000022−220000−22−226−6−6600000000000000000000000000
χ5444-4-400-2040-4-2220000000-2223−2323−2300000−222200002−22−2−666−600000000000000000000000000
χ5544-4-400-2040-4-2220000000-22−2323−23230000022−220000−22−22−666−600000000000000000000000000
χ5644-4-400-2040-4-2220000000-22−2323−232300000−222200002−22−26−6−6600000000000000000000000000
χ5744-4-400-20-404-22200000002-223−23−23230000000−2i22i200i6−i6−i6i6i2−i2i2−i200000000000000000000000000
χ5844-4-400-20-404-22200000002-223−23−232300000002i2−2i200−i6i6i6−i6−i2i2−i2i200000000000000000000000000
χ5944-4-400-20-404-22200000002-2−232323−230000000−2i22i200−i6i6i6−i6i2−i2i2−i200000000000000000000000000
χ6044-4-400-20-404-22200000002-2−232323−2300000002i2−2i200i6−i6−i6i6−i2i2−i2i200000000000000000000000000
χ614-44-400440-40-44-40000004000000-4000000000000000000000022−2222−22000000000000000000
χ624-44-400440-40-44-40000004000000-40000000000000000000000−2222−2222000000000000000000
χ634-44-4004-4040-44-4000000-400000040000000000000000000000−2i22i22i2−2i2000000000000000000
χ644-44-4004-4040-44-4000000-4000000400000000000000000000002i2−2i2−2i22i2000000000000000000
χ654-4-444-440000-4-4400004-40000000000000000000000000022−2222−220000000000000000000000
χ664-4-444-440000-4-4400004-400000000000000000000000000−2222−22220000000000000000000000
χ674-4-44-4440000-4-440000-440000000000000000000000000022−22−22220000000000000000000000
χ684-4-44-4440000-4-440000-4400000000000000000000000000−222222−220000000000000000000000
χ698-88-800-480-804-44000000-4000000400000000000000000000000000000000000000000000
χ708-88-800-4-80804-440000004000000-400000000000000000000000000000000000000000000
χ718-8-888-8-4000044-40000-440000000000000000000000000000000000000000000000000000
χ728-8-88-88-4000044-400004-40000000000000000000000000000000000000000000000000000

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