Finite Group Databasebeta

← Group #10772498

Character table — Group #10772498

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888881212121212121212161616161616161616161616242424242424242424242424
order122222344444444666444444661212121212121212441212121212121212121288888888246688121224242424244444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111-1-11-1-111111111111-1-11-1-1-1-11-1-1-1-1111111111111-1-111-1-1-1-1-1-111-111-1-1-1-1-1
χ6111111111111111111-1-11-1-111111111111-1-11-1-1-1-11-1-1-1-111111111-1-1-1-111-1-1111111-1-11-1-11-1-1-1-1
χ7111111111111111111-1-11-1-111111111111-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11-1-111111
χ8111111111111111111-1-11-1-111111111111-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-111-11111
χ91111-1-11-1-11-1-111111111-1-1-11-1-111-1-1-1-111-11-111-1-1111-1-11111-1-1-1-11-1111-1-1-111-1-11-111-1-1-1111-1-1
χ101111-1-11-1-11-1-111111111-1-1-11-1-111-1-1-1-111-11-111-1-1111-1-11111-1-1-1-1-11-1-1-1111-1-111-11-1-1111-111-1-1
χ111111-1-11-1-11-1-111111111-1-1-11-1-111-1-1-1-111-11-111-1-1111-1-1-1-1-1-111111-1111-1-1-111-1-1-11-1-1111-1-1-111
χ121111-1-11-1-11-1-111111111-1-1-11-1-111-1-1-1-111-11-111-1-1111-1-1-1-1-1-11111-11-1-1-1111-1-1111-111-1-1-11-1-111
χ131111-1-11-1-11-1-1111111-1-1-1111-1-111-1-1-1-1111-1-1-1-1111-1-1111111-1-1-1-11-111-11-1-1-1-111-11111-1-1-1-1-111
χ141111-1-11-1-11-1-1111111-1-1-1111-1-111-1-1-1-1111-1-1-1-1111-1-1111111-1-1-1-1-11-1-11-11111-1-11-1-1-1-1111-1-111
χ151111-1-11-1-11-1-1111111-1-1-1111-1-111-1-1-1-1111-1-1-1-1111-1-111-1-1-1-111111-111-11-1-1-1-1111-1-1-1-111111-1-1
χ161111-1-11-1-11-1-1111111-1-1-1111-1-111-1-1-1-1111-1-1-1-1111-1-111-1-1-1-11111-11-1-11-11111-1-1-11111-1-1-111-1-1
χ17222222222-2-2-2-2-2-222200-200222-2-2-2-222-2-200-200002000000000000000000000000002-202-200000
χ18222222222-2-2-2-2-2-222200-200222-2-2-2-222-2-200-20000200000000000000000000000000-220-2200000
χ192222222-2-2222-2-2222200-200-2222222-2-2-2-200-20000-20000000000000000000000002200-200-20000
χ202222222-2-2222-2-2222200-200-2222222-2-2-2-200-20000-2000000000000000000000000-2-20020020000
χ212222222-2-2-2-2-222-2222222-2-2-222-2-2-2-2-2-2222-22-2-2-2-2-2222200000000000000000000000000000000
χ222222222-2-2-2-2-222-2222-2-2222-222-2-2-2-2-2-222-2222222-2-2-2-2-200000000000000000000000000000000
χ23222222-122222222-1-1-1222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000000022-1-122-1-1-1-1-1-1000000000000
χ24222222-122222222-1-1-1222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000-2-211-2-2111111000000000000
χ25222222-122222222-1-1-1-2-22-2-22-1-1-1-1-1-1-1-1-1-1-2-2-11111-111110000000022-1-1-2-2-1-11111000000000000
χ26222222-122222222-1-1-1-2-22-2-22-1-1-1-1-1-1-1-1-1-1-2-2-11111-1111100000000-2-2112211-1-1-1-1000000000000
χ27222222-1-2-2-2-2-222-2-1-1-1222-2-2-2-1-1111111-1-12-2-111111-1-1-1-10000000000−i3i300−i3i3−i3i3−i3i3000000000000
χ28222222-1-2-2-2-2-222-2-1-1-1222-2-2-2-1-1111111-1-12-2-111111-1-1-1-10000000000i3−i300i3−i3i3−i3i3−i3000000000000
χ29222222-1-2-2-2-2-222-2-1-1-1-2-2222-2-1-1111111-1-1-22-1-1-1-1-1111110000000000−i3i300−i3i3i3−i3i3−i3000000000000
χ30222222-1-2-2-2-2-222-2-1-1-1-2-2222-2-1-1111111-1-1-22-1-1-1-1-1111110000000000i3−i300i3−i3−i3i3−i3i3000000000000
χ312222-2-22222-2-2-2-2222200200-2-2-222-2-222-2-20020000-20000000000000000000000002-200200-20000
χ322222-2-22222-2-2-2-2222200200-2-2-222-2-222-2-20020000-2000000000000000000000000-2200-20020000
χ332222-2-2222-22222-222222-222-2-2-2-2-2222222-2-2-2-2-222-222-2-200000000000000000000000000000000
χ342222-2-2222-22222-2222-2-2-2-2-2-2-2-2-2-222222222-222-2-2-2-2-22200000000000000000000000000000000
χ352222-2-22-2-2-222-2-2-2222002002-2-2-2-222-2-2-2-200200002000000000000000000000000002-20-2200000
χ362222-2-22-2-2-222-2-2-2222002002-2-2-2-222-2-2-2-20020000200000000000000000000000000-2202-200000
χ372222-2-2-122-22222-2-1-1-122-222-21111-1-1-1-1-1-1-2-2111-1-11-1-1110000000000−i3i300i3−i3−i3i3i3−i3000000000000
χ382222-2-2-122-22222-2-1-1-122-222-21111-1-1-1-1-1-1-2-2111-1-11-1-1110000000000i3−i300−i3i3i3−i3−i3i3000000000000
χ392222-2-2-122-22222-2-1-1-1-2-2-2-2-2-21111-1-1-1-1-1-1221-1-111111-1-10000000000−i3i300i3−i3i3−i3−i3i3000000000000
χ402222-2-2-122-22222-2-1-1-1-2-2-2-2-2-21111-1-1-1-1-1-1221-1-111111-1-10000000000i3−i300−i3i3−i3i3i3−i3000000000000
χ412222-2-2-1-2-22-2-2222-1-1-122-2-2-2211-1-11111-1-1-221-1-111-1-1-111000000002-2-1-12-211-1-111000000000000
χ422222-2-2-1-2-22-2-2222-1-1-122-2-2-2211-1-11111-1-1-221-1-111-1-1-11100000000-2211-22-1-111-1-1000000000000
χ432222-2-2-1-2-22-2-2222-1-1-1-2-2-222211-1-11111-1-12-2111-1-1-111-1-1000000002-2-1-1-221111-1-1000000000000
χ442222-2-2-1-2-22-2-2222-1-1-1-2-2-222211-1-11111-1-12-2111-1-1-111-1-100000000-22112-2-1-1-1-111000000000000
χ452-2-220022i−2i02i−2i2-20-22-22i−2i02-2000002i−2i2i−2i2-2000002-202i−2i00−i2−i2i2i222−2−2000000000000000000002−2−i2i2
χ462-2-220022i−2i02i−2i2-20-22-22i−2i02-2000002i−2i2i−2i2-2000002-202i−2i00i2i2−i2−i2−2−22200000000000000000000−22i2−i2
χ472-2-220022i−2i02i−2i2-20-22-2−2i2i0-22000002i−2i2i−2i2-200000-220−2i2i00−i2−i2i2i222−2−200000000000000000000−22i2−i2
χ482-2-220022i−2i02i−2i2-20-22-2−2i2i0-22000002i−2i2i−2i2-200000-220−2i2i00i2i2−i2−i2−2−222000000000000000000002−2−i2i2
χ492-2-22002−2i2i0−2i2i2-20-22-22i−2i0-2200000−2i2i−2i2i2-200000-2202i−2i00−i2−i2i2i2−2−222000000000000000000002−2i2−i2
χ502-2-22002−2i2i0−2i2i2-20-22-22i−2i0-2200000−2i2i−2i2i2-200000-2202i−2i00i2i2−i2−i222−2−200000000000000000000−22−i2i2
χ512-2-22002−2i2i0−2i2i2-20-22-2−2i2i02-200000−2i2i−2i2i2-2000002-20−2i2i00−i2−i2i2i2−2−22200000000000000000000−22−i2i2
χ522-2-22002−2i2i0−2i2i2-20-22-2−2i2i02-200000−2i2i−2i2i2-2000002-20−2i2i00i2i2−i2−i222−2−2000000000000000000002−2i2−i2
χ53444444-244-4-4-4-4-4-4-2-2-200-4004-2-22222-2-2220020000-2000000000000000000000000000000000000
χ54444444-2-4-4444-4-44-2-2-200-400-4-2-2-2-2-2-2222200200002000000000000000000000000000000000000
χ554444-4-4-2444-4-4-4-44-2-2-200400-422-2-222-2-22200-200002000000000000000000000000000000000000
χ564444-4-4-2-4-4-444-4-4-4-2-2-20040042222-2-2222200-20000-2000000000000000000000000000000000000
χ5744-4-44-4400000000-4-440000004-4000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ5844-4-44-4400000000-4-440000004-400000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ5944-4-4-44400000000-4-44000000-44000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ6044-4-4-44400000000-4-44000000-4400000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ614-44-40040040000-44-4-4000000004-400000000000000000022−22−22220000000000000000000000000000
χ624-44-40040040000-44-4-4000000004-4000000000000000000−222222−220000000000000000000000000000
χ634-44-400400-4000044-4-400000000-440000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ644-44-400400-4000044-4-400000000-4400000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ654-4-440044i−4i0−4i4i-440-44-40000000000−4i4i4i−4i-4400000000000000000000000000000000000000000000
χ664-4-44004−4i4i04i−4i-440-44-400000000004i−4i−4i4i-4400000000000000000000000000000000000000000000
χ674-4-4400-24i−4i04i−4i4-402-224i−4i04-400000−2i2i−2i2i-2200000-220−2i2i0000000000000000000000000000000000
χ684-4-4400-24i−4i04i−4i4-402-22−4i4i0-4400000−2i2i−2i2i-22000002-202i−2i0000000000000000000000000000000000
χ694-4-4400-24i−4i0−4i4i-4402-2200000000002i−2i−2i2i2-2000−2i32i30000023−2300000000000000000000000000000000
χ704-4-4400-24i−4i0−4i4i-4402-2200000000002i−2i−2i2i2-20002i3−2i300000−232300000000000000000000000000000000
χ714-4-4400-2−4i4i04i−4i-4402-220000000000−2i2i2i−2i2-2000−2i32i300000−232300000000000000000000000000000000
χ724-4-4400-2−4i4i04i−4i-4402-220000000000−2i2i2i−2i2-20002i3−2i30000023−2300000000000000000000000000000000
χ734-4-4400-2−4i4i0−4i4i4-402-224i−4i0-44000002i−2i2i−2i-22000002-20−2i2i0000000000000000000000000000000000
χ744-4-4400-2−4i4i0−4i4i4-402-22−4i4i04-4000002i−2i2i−2i-2200000-2202i−2i0000000000000000000000000000000000
χ7588-8-88-8-40000000044-4000000-440000000000000000000000000000000000000000000000000000
χ7688-8-8-88-40000000044-40000004-40000000000000000000000000000000000000000000000000000
χ778-88-800-40080000-8-44400000000-4400000000000000000000000000000000000000000000000000
χ788-88-800-400-800008-444000000004-400000000000000000000000000000000000000000000000000

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