Finite Group Databasebeta

← Group #10698005

Character table — Group #10698005

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order122222223444444444444666666688888888121212121212121212121212242424242424242424242424242424248888888888888888444412121212121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ922222222222-2-2-2-2-2-222-2-22222222000000002222-2-2-2-2-2-2-2-200000000000000002222-2-2-2-2000000000000000000000000
χ1022222222222-2-2-2-2-2-222-2-22222222000000002222-2-2-2-2-2-2-2-20000000000000000-2-2-2-22222000000000000000000000000
χ11222222222-2-222-2-2-2-2-2-222222222200000000-2-2-2-22222-2-2-2-20000000000000000000000002222-2-2-2-20000000000000000
χ12222222222-2-222-2-2-2-2-2-222222222200000000-2-2-2-22222-2-2-2-2000000000000000000000000-2-2-2-222220000000000000000
χ13222222222-2-2-2-22222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ14222222222-2-2-2-22222-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ1522222222-1222222222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ1622222222-1222222222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ1722222222-1222222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ1822222222-1222222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ1922222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000000000−i3−i3i3i3−i3−i3i3i30000
χ2022222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000000000i3i3−i3−i3i3i3−i3−i30000
χ2122222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-111111111-1-1-1-1-1-1-1-100000000000000000000−i3−i3i3i3i3i3−i3−i30000
χ2222222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-111111111-1-1-1-1-1-1-1-100000000000000000000i3i3−i3−i3−i3−i3i3i30000
χ23222-22-2-2-222-20000002-20022-2-22-2-222−2−222−2−222-2-2000000002222−2−2−2−22222−2−2−2−2000022-2-222−2−222−2−20000000000000000
χ24222-22-2-2-222-20000002-20022-2-22-2-222−2−222−2−222-2-2000000002222−2−2−2−22222−2−2−2−20000-2-222−2−222−2−2220000000000000000
χ25222-22-2-2-222-20000002-20022-2-22-2-2−2−222−2−22222-2-200000000−2−2−2−22222−2−2−2−22222000022-2-2−2−222−2−2220000000000000000
χ26222-22-2-2-222-20000002-20022-2-22-2-2−2−222−2−22222-2-200000000−2−2−2−22222−2−2−2−222220000-2-22222−2−222−2−20000000000000000
χ27222-22-2-2-22-22000000-220022-2-22-2-222−2−2−2−222-2-222000000002222−2−2−2−2−2−2−2−2222222-2-2000022−2−2−2−2220000000000000000
χ28222-22-2-2-22-22000000-220022-2-22-2-222−2−2−2−222-2-222000000002222−2−2−2−2−2−2−2−22222-2-2220000−2−22222−2−20000000000000000
χ29222-22-2-2-22-22000000-220022-2-22-2-2−2−22222−2−2-2-22200000000−2−2−2−222222222−2−2−2−222-2-20000−2−22222−2−20000000000000000
χ30222-22-2-2-22-22000000-220022-2-22-2-2−2−22222−2−2-2-22200000000−2−2−2−222222222−2−2−2−2-2-222000022−2−2−2−2220000000000000000
χ3122-22-2-2-22200002-22-200002-22-2-22-200002i−2i2i−2i000000002-22-2000000002i2i−2i−2i2i2i−2i−2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ3222-22-2-2-22200002-22-200002-22-2-22-200002i−2i2i−2i000000002-22-2000000002i2i−2i−2i2i2i−2i−2i−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ3322-22-2-2-22200002-22-200002-22-2-22-20000−2i2i−2i2i000000002-22-200000000−2i−2i2i2i−2i−2i2i2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ3422-22-2-2-22200002-22-200002-22-2-22-20000−2i2i−2i2i000000002-22-200000000−2i−2i2i2i−2i−2i2i2i−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ3522-22-2-2-2220000-22-2200002-22-2-22-22i−2i2i−2i000000000000-22-222i2i−2i−2i2i2i−2i−2i000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ3622-22-2-2-2220000-22-2200002-22-2-22-22i−2i2i−2i000000000000-22-222i2i−2i−2i2i2i−2i−2i00000000−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ3722-22-2-2-2220000-22-2200002-22-2-22-2−2i2i−2i2i000000000000-22-22−2i−2i2i2i−2i−2i2i2i000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ3822-22-2-2-2220000-22-2200002-22-2-22-2−2i2i−2i2i000000000000-22-22−2i−2i2i2i−2i−2i2i2i00000000−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ3922-2-2-222-22002-20000002-22-2-22-2-22−i2i2i2−i2−i2i2i2−i2000022-2-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i22−2−222−2−2200002i−2i−2i2i0000000000000000
χ4022-2-2-222-22002-20000002-22-2-22-2-22−i2i2i2−i2−i2i2i2−i2000022-2-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−222−2−222−20000−2i2i2i−2i0000000000000000
χ4122-2-2-222-22002-20000002-22-2-22-2-22i2−i2−i2i2i2−i2−i2i2000022-2-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i22−2−222−2−220000−2i2i2i−2i0000000000000000
χ4222-2-2-222-22002-20000002-22-2-22-2-22i2−i2−i2i2i2−i2−i2i2000022-2-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−222−2−222−200002i−2i−2i2i0000000000000000
χ4322-2-2-222-2200-22000000-222-2-22-2-22−i2i2i2−i2i2−i2−i2i20000-2-2220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i22−2−22−222−22i−2i−2i2i00000000000000000000
χ4422-2-2-222-2200-22000000-222-2-22-2-22−i2i2i2−i2i2−i2−i2i20000-2-2220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−222−22−2−22−2i2i2i−2i00000000000000000000
χ4522-2-2-222-2200-22000000-222-2-22-2-22i2−i2−i2i2−i2i2i2−i20000-2-2220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i22−2−22−222−2−2i2i2i−2i00000000000000000000
χ4622-2-2-222-2200-22000000-222-2-22-2-22i2−i2−i2i2−i2i2i2−i20000-2-2220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−222−22−2−222i−2i−2i2i00000000000000000000
χ472-2-2-222-222222222-2-2-2-2-2-2-2-2-2-2222000000002-22-22-22-222-2-2000000000000000000000000000000000000000000002i−2i00
χ482-2-2-222-222222222-2-2-2-2-2-2-2-2-2-2222000000002-22-22-22-222-2-200000000000000000000000000000000000000000000−2i2i00
χ492-2-2-222-22222-2-2-2-222-2-222-2-2-2-2222000000002-22-2-22-22-2-222000000000000000000000000000000002-2002-22-200000000
χ502-2-2-222-22222-2-2-2-222-2-222-2-2-2-2222000000002-22-2-22-22-2-22200000000000000000000000000000000-2200-22-2200000000
χ512-2-2-222-222-2-222-2-22222-2-2-2-2-2-222200000000-22-222-22-2-2-22200000000000000000000000000000000002-200002-22-20000
χ522-2-2-222-222-2-222-2-22222-2-2-2-2-2-222200000000-22-222-22-2-2-2220000000000000000000000000000000000-220000-22-220000
χ532-2-2-222-222-2-2-2-222-2-22222-2-2-2-222200000000-22-22-22-2222-2-200000000000000000000000000000000000000000000002-2
χ542-2-2-222-222-2-2-2-222-2-22222-2-2-2-222200000000-22-22-22-2222-2-20000000000000000000000000000000000000000000000-22
χ552-2-2-222-22-122-2-2-2-222-2-2221111-1-1-100000000-11-111-11-111-1-1−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i300000000000000002-200-11-11−i3i3i3−i30000
χ562-2-2-222-22-122-2-2-2-222-2-2221111-1-1-100000000-11-111-11-111-1-1−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000000000000000-22001-11-1i3−i3−i3i30000
χ572-2-2-222-22-122-2-2-2-222-2-2221111-1-1-100000000-11-111-11-111-1-1i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i300000000000000002-200-11-11i3−i3−i3i30000
χ582-2-2-222-22-122-2-2-2-222-2-2221111-1-1-100000000-11-111-11-111-1-1i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000000000000000-22001-11-1−i3i3i3−i30000
χ592-2-2-222-22-1-2-222-2-22222-2-21111-1-1-1000000001-11-1-11-1111-1-1−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i30000000000000000002-2−i3i3i3−i3-11-110000
χ602-2-2-222-22-1-2-222-2-22222-2-21111-1-1-1000000001-11-1-11-1111-1-1−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3000000000000000000-22i3−i3−i3i31-11-10000
χ612-2-2-222-22-1-2-222-2-22222-2-21111-1-1-1000000001-11-1-11-1111-1-1i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i30000000000000000002-2i3−i3−i3i3-11-110000
χ622-2-2-222-22-1-2-222-2-22222-2-21111-1-1-1000000001-11-1-11-1111-1-1i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3000000000000000000-22−i3i3i3−i31-11-10000
χ6344444444-244-4-4-4-4-4-444-4-4-2-2-2-2-2-2-200000000-2-2-2-222222222000000000000000000000000000000000000000000000000
χ6444444444-2-4-444-4-4-4-4-4-444-2-2-2-2-2-2-2000000002222-2-2-2-22222000000000000000000000000000000000000000000000000
χ65444-44-4-4-4-24-40000004-400-2-222-2222222−22−222222−22−22-2-22200000000−2−2−2−22222−2−2−2−2222200000000000000000000000000000000
χ66444-44-4-4-4-24-40000004-400-2-222-222−22−222222−22−222222-2-222000000002222−2−2−2−22222−2−2−2−200000000000000000000000000000000
χ67444-44-4-4-4-2-44000000-4400-2-222-2222222−22−22−22−22222222-2-200000000−2−2−2−222222222−2−2−2−200000000000000000000000000000000
χ68444-44-4-4-4-2-44000000-4400-2-222-222−22−2222222222−22−2222-2-2000000002222−2−2−2−2−2−2−2−2222200000000000000000000000000000000
χ6944-44-4-4-44-200004-44-40000-22-222-2200004i−4i4i−4i00000000-22-2200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ7044-44-4-4-44-200004-44-40000-22-222-220000−4i4i−4i4i00000000-22-22000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ7144-44-4-4-44-20000-44-440000-22-222-224i−4i4i−4i0000000000002-22-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ7244-44-4-4-44-20000-44-440000-22-222-22−4i4i−4i4i0000000000002-22-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ7344-4-4-444-4-2004-40000004-4-222-222-2−2i22i22i2−2i2−2i22i22i2−2i20000-2-2220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ7444-4-4-444-4-2004-40000004-4-222-222-22i2−2i2−2i22i22i2−2i2−2i22i20000-2-2220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
χ7544-4-4-444-4-200-44000000-44-222-222-2−2i22i22i2−2i22i2−2i2−2i22i2000022-2-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
χ7644-4-4-444-4-200-44000000-44-222-222-22i2−2i2−2i22i2−2i22i22i2−2i2000022-2-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ774-444-44-4-44004-4000000-44-444-4-4-440000000000004-4-440000000000000000000000000000000000000000000000000000
χ784-444-44-4-4400-440000004-4-444-4-4-44000000000000-444-40000000000000000000000000000000000000000000000000000
χ794-444-44-4-4-2004-4000000-442-2-2222-2000000000000-222-200006−6−66−666−6−666−66−6−6600000000000000000000000000000000
χ804-444-44-4-4-2004-4000000-442-2-2222-2000000000000-222-20000−666−66−6−666−6−66−666−600000000000000000000000000000000
χ814-444-44-4-4-200-440000004-42-2-2222-20000000000002-2-2200006−6−66−666−66−6−66−666−600000000000000000000000000000000
χ824-444-44-4-4-200-440000004-42-2-2222-20000000000002-2-220000−666−66−6−66−666−66−6−6600000000000000000000000000000000
χ834-44-4-4-444400004-4-440000-44-44-44-400000000000000004-4-44000000000000000000000000000000000000000000000000
χ844-44-4-4-44440000-444-40000-44-44-44-40000000000000000-444-4000000000000000000000000000000000000000000000000
χ854-44-4-4-444-200004-4-4400002-22-22-220000000000000000-222-223−23−232323−23−23230000000000000000000000000000000000000000
χ864-44-4-4-444-200004-4-4400002-22-22-220000000000000000-222-2−232323−23−232323−230000000000000000000000000000000000000000
χ874-44-4-4-444-20000-444-400002-22-22-2200000000000000002-2-220000000023−23−232323−23−232300000000000000000000000000000000
χ884-44-4-4-444-20000-444-400002-22-22-2200000000000000002-2-2200000000−232323−23−232323−2300000000000000000000000000000000
χ894-4-444-44-444-4000000-4400-4-4444-4-4000000004-4-4400000000000000000000000000000000000000000000000000000000
χ904-4-444-44-44-440000004-400-4-4444-4-400000000-444-400000000000000000000000000000000000000000000000000000000
χ914-4-444-44-4-24-4000000-440022-2-2-22200000000-222-200000000i6−i6i6−i6−i6i6−i6i6i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000
χ924-4-444-44-4-24-4000000-440022-2-2-22200000000-222-200000000−i6i6−i6i6i6−i6i6−i6−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000
χ934-4-444-44-4-2-440000004-40022-2-2-222000000002-2-2200000000i6−i6i6−i6−i6i6−i6i6−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000
χ944-4-444-44-4-2-440000004-40022-2-2-222000000002-2-2200000000−i6i6−i6i6i6−i6i6−i6i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000
χ954-4-4-444-44-2444444-4-4-4-4-4-42222-2-2-200000000-22-22-22-22-2-222000000000000000000000000000000000000000000000000
χ964-4-4-444-44-2-4-4-4-444-4-444442222-2-2-2000000002-22-22-22-2-2-222000000000000000000000000000000000000000000000000

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