Finite Group Databasebeta

← Group #10711558

Character table — Group #10711558

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order1222223444444446666666888888884488881212121212121212121212122424242424242424242424242424242416161616161616161616161616161616444412121212121212128888
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
χ511111111-1-1-1-11111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ611111111-1-1-1-11111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ711111111-1-1-1-11111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ811111111-1-1-1-11111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91111-1-11-1111111-1-1-1111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−ii−ii−i
χ101111-1-11-1111111-1-1-1111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−ii−ii
χ111111-1-11-1111111-1-1-1111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111i−ii−iii−i−iii−i−i−ii−ii
χ121111-1-11-1111111-1-1-1111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−ii−ii−i−iii−i−iiii−ii−i
χ131111-1-11-1-1-1-1-111-1-1-1111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iiii−i−ii
χ141111-1-11-1-1-1-1-111-1-1-1111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i−iii−i
χ151111-1-11-1-1-1-1-111-1-1-1111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1i−i−iiii−i−i−i−iii−iii−i
χ161111-1-11-1-1-1-1-111-1-1-1111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−iii−i−i−iiiii−i−ii−i−ii
χ172222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1822222222-2-2-2-222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ192222222-222-2-2-2-2-22222222000000002-20000-2-222-2-222-2-2-2-20000000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ202222222-222-2-2-2-2-22222222000000002-20000-2-222-2-222-2-2-2-20000000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ212222222-2-2-222-2-2-2222222200000000-220000-2-2-2-222-2-222-2-20000000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ222222222-2-2-222-2-2-2222222200000000-220000-2-2-2-222-2-222-2-20000000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ23222222-122222222-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ24222222-122222222-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ25222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ26222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ27222222-12-2-2-2-2222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-222-1-111111111-1-111111111-1-1-1-1-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ28222222-12-2-2-2-2222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-222-1-111111111-1-111111111-1-1-1-1-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ29222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-22222-2-222-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-111110000
χ30222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-22222-2-222-2-2-1-111111111-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-10000
χ312222-2-22222-2-2-2-22-2-2222-2-200000000-2200002222-2-2-2-222-2-20000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ322222-2-22222-2-2-2-22-2-2222-2-200000000-2200002222-2-2-2-222-2-20000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ332222-2-222-2-222-2-22-2-2222-2-2000000002-2000022-2-22222-2-2-2-20000000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ342222-2-222-2-222-2-22-2-2222-2-2000000002-2000022-2-22222-2-2-2-20000000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ352222-2-22-2222222-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ362222-2-22-2-2-2-2-222-2-2-2222-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2222222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ372222-2-2-1-2222222-211-1-1-11122222222-2-2-2-2-2-211-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000000000002i−2i2i−2i−i−iii−i−iii0000
χ382222-2-2-1-2222222-211-1-1-11122222222-2-2-2-2-2-211-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111110000000000000000−2i2i−2i2iii−i−iii−i−i0000
χ392222-2-2-1-2222222-211-1-1-111-2-2-2-2-2-2-2-2-2-2222211-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1000000000000000000003−3−333−3−330000
χ402222-2-2-1-2222222-211-1-1-111-2-2-2-2-2-2-2-2-2-2222211-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−333−3−333−30000
χ412222-2-2-1-2-2-2-2-222-211-1-1-1112222-2-2-2-22222-2-2111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111000000000000000000003−3−33−333−30000
χ422222-2-2-1-2-2-2-2-222-211-1-1-1112222-2-2-2-22222-2-2111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−333−33−3−330000
χ432222-2-2-1-2-2-2-2-222-211-1-1-111-2-2-2-2222222-2-222111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ442222-2-2-1-2-2-2-2-222-211-1-1-111-2-2-2-2222222-2-222111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii0000
χ4522-2-22-22200002-2-2222-2-2-2-222-2-2000000002-22-2000000002-20000000022-2-222-2-22−22−22−22−22−22−22−22−20000000000000000
χ4622-2-22-22200002-2-2222-2-2-2-222-2-2000000002-22-2000000002-20000000022-2-222-2-2−22−22−22−22−22−22−22−220000000000000000
χ4722-2-22-22200002-2-2222-2-2-2-2-2-22200000000-222-2000000002-200000000-2-222-2-2222−22−22−22−2−22−22−22−220000000000000000
χ4822-2-22-22200002-2-2222-2-2-2-2-2-22200000000-222-2000000002-200000000-2-222-2-222−22−22−22−222−22−22−22−20000000000000000
χ4922-2-22-22-20000-222222-2-2-2-2000022-2-2002-200-2200000000-2222-2-222-2-200000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ5022-2-22-22-20000-222222-2-2-2-2000022-2-2002-200-2200000000-2222-2-222-2-20000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ5122-2-22-22-20000-222222-2-2-2-20000-2-22200-2200-2200000000-22-2-222-2-222000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ5222-2-22-22-20000-222222-2-2-2-20000-2-22200-2200-2200000000-22-2-222-2-22200000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ5322-2-2-22220000-22-2-2-22-2-222000022-2-200-22002-200000000-2222-2-2-2-22200000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ5422-2-2-22220000-22-2-2-22-2-222000022-2-200-22002-200000000-2222-2-2-2-2220000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ5522-2-2-22220000-22-2-2-22-2-2220000-2-222002-2002-200000000-22-2-22222-2-2000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ5622-2-2-22220000-22-2-2-22-2-2220000-2-222002-2002-200000000-22-2-22222-2-200000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ5722-2-2-222-200002-22-2-22-2-22222-2-200000000-22-22000000002-20000000022-2-2-2-2222−22−2−22−222−22−2−22−220000000000000000
χ5822-2-2-222-200002-22-2-22-2-22222-2-200000000-22-22000000002-20000000022-2-2-2-222−22−222−22−2−22−222−22−20000000000000000
χ5922-2-2-222-200002-22-2-22-2-222-2-222000000002-2-22000000002-200000000-2-22222-2-22−22−2−22−22−22−222−22−20000000000000000
χ6022-2-2-222-200002-22-2-22-2-222-2-222000000002-2-22000000002-200000000-2-22222-2-2−22−222−22−22−22−2−22−220000000000000000
χ61444444-2-444-4-4-4-4-4-2-2-2-2-2-2-2000000004-4000022-2-222-2-22222000000000000000000000000000000000000000000000000
χ62444444-2-4-4-444-4-4-4-2-2-2-2-2-2-200000000-4400002222-2-222-2-222000000000000000000000000000000000000000000000000
χ634444-4-4-2444-4-4-4-4422-2-2-22200000000-440000-2-2-2-22222-2-222000000000000000000000000000000000000000000000000
χ644444-4-4-24-4-444-4-4422-2-2-222000000004-40000-2-222-2-2-2-22222000000000000000000000000000000000000000000000000
χ6544-4-44-4-2400004-4-4-2-2-2222244-4-4000000004-4-2200000000-2200000000-2-222-2-22200000000000000000000000000000000
χ6644-4-44-4-2400004-4-4-2-2-22222-4-44400000000-44-2200000000-220000000022-2-222-2-200000000000000000000000000000000
χ6744-4-44-4-2-40000-444-2-2-22222000044-4-4004-4002-2000000002-2-2-222-2-2220000000000000000000000000000000000000000
χ6844-4-44-4-2-40000-444-2-2-222220000-4-44400-44002-2000000002-222-2-222-2-20000000000000000000000000000000000000000
χ6944-4-4-44-240000-44-422-222-2-2000044-4-400-4400-22000000002-2-2-22222-2-20000000000000000000000000000000000000000
χ7044-4-4-44-240000-44-422-222-2-20000-4-444004-400-22000000002-222-2-2-2-2220000000000000000000000000000000000000000
χ7144-4-4-44-2-400004-4422-222-2-244-4-400000000-442-200000000-2200000000-2-22222-2-200000000000000000000000000000000
χ7244-4-4-44-2-400004-4422-222-2-2-4-444000000004-42-200000000-220000000022-2-2-2-22200000000000000000000000000000000
χ734-44-40040004-400000-44-400−2i22i2−2i22i2−2i22i2−2i22i200000000004-4000000−2i22i2−2i22i20000−2i22i2−2i22i2000000000000000000000000000000000000
χ744-44-40040004-400000-44-4002i2−2i22i2−2i22i2−2i22i2−2i200000000004-40000002i2−2i22i2−2i200002i2−2i22i2−2i2000000000000000000000000000000000000
χ754-44-4004000-4400000-44-400−2i22i2−2i22i22i2−2i22i2−2i20000000000-440000002i2−2i22i2−2i20000−2i22i2−2i22i2000000000000000000000000000000000000
χ764-44-4004000-4400000-44-4002i2−2i22i2−2i2−2i22i2−2i22i20000000000-44000000−2i22i2−2i22i200002i2−2i22i2−2i2000000000000000000000000000000000000
χ774-44-400-20004-4000−2i32i32-22−2i32i3−2i22i2−2i22i2−2i22i2−2i22i20000000000-2200−2i32i300i2−i2i2−i26−66−6i2−i2i2−i26−66−600000000000000000000000000000000
χ784-44-400-20004-4000−2i32i32-22−2i32i32i2−2i22i2−2i22i2−2i22i2−2i20000000000-2200−2i32i300−i2i2−i2i2−66−66−i2i2−i2i2−66−6600000000000000000000000000000000
χ794-44-400-20004-40002i3−2i32-222i3−2i3−2i22i2−2i22i2−2i22i2−2i22i20000000000-22002i3−2i300i2−i2i2−i2−66−66i2−i2i2−i2−66−6600000000000000000000000000000000
χ804-44-400-20004-40002i3−2i32-222i3−2i32i2−2i22i2−2i22i2−2i22i2−2i20000000000-22002i3−2i300−i2i2−i2i26−66−6−i2i2−i2i26−66−600000000000000000000000000000000
χ814-44-400-2000-44000−2i32i32-22−2i32i3−2i22i2−2i22i22i2−2i22i2−2i200000000002-2002i3−2i300−i2i2−i2i2−66−66i2−i2i2−i26−66−600000000000000000000000000000000
χ824-44-400-2000-44000−2i32i32-22−2i32i32i2−2i22i2−2i2−2i22i2−2i22i200000000002-2002i3−2i300i2−i2i2−i26−66−6−i2i2−i2i2−66−6600000000000000000000000000000000
χ834-44-400-2000-440002i3−2i32-222i3−2i3−2i22i2−2i22i22i2−2i22i2−2i200000000002-200−2i32i300−i2i2−i2i26−66−6i2−i2i2−i2−66−6600000000000000000000000000000000
χ844-44-400-2000-440002i3−2i32-222i3−2i32i2−2i22i2−2i2−2i22i2−2i22i200000000002-200−2i32i300i2−i2i2−i2−66−66−i2i2−i2i26−66−600000000000000000000000000000000
χ854-4-4400404-40000000-4-4400−2i22i22i2−2i2−2i22i22i2−2i2000000004-400000000−2i22i22i2−2i20000−2i22i22i2−2i2000000000000000000000000000000000000
χ864-4-4400404-40000000-4-44002i2−2i2−2i22i22i2−2i2−2i22i2000000004-4000000002i2−2i2−2i22i200002i2−2i2−2i22i2000000000000000000000000000000000000
χ874-4-440040-440000000-4-4400−2i22i22i2−2i22i2−2i2−2i22i200000000-44000000002i2−2i2−2i22i20000−2i22i22i2−2i2000000000000000000000000000000000000
χ884-4-440040-440000000-4-44002i2−2i2−2i22i2−2i22i22i2−2i200000000-4400000000−2i22i22i2−2i200002i2−2i2−2i22i2000000000000000000000000000000000000
χ894-4-4400-204-400000−2i32i322-22i3−2i3−2i22i22i2−2i2−2i22i22i2−2i200000000-2200−2i32i30000i2−i2−i2i26−6−66i2−i2−i2i26−6−6600000000000000000000000000000000
χ904-4-4400-204-400000−2i32i322-22i3−2i32i2−2i2−2i22i22i2−2i2−2i22i200000000-2200−2i32i30000−i2i2i2−i2−666−6−i2i2i2−i2−666−600000000000000000000000000000000
χ914-4-4400-204-4000002i3−2i322-2−2i32i3−2i22i22i2−2i2−2i22i22i2−2i200000000-22002i3−2i30000i2−i2−i2i2−666−6i2−i2−i2i2−666−600000000000000000000000000000000
χ924-4-4400-204-4000002i3−2i322-2−2i32i32i2−2i2−2i22i22i2−2i2−2i22i200000000-22002i3−2i30000−i2i2i2−i26−6−66−i2i2i2−i26−6−6600000000000000000000000000000000
χ934-4-4400-20-4400000−2i32i322-22i3−2i3−2i22i22i2−2i22i2−2i2−2i22i2000000002-2002i3−2i30000−i2i2i2−i2−666−6i2−i2−i2i26−6−6600000000000000000000000000000000
χ944-4-4400-20-4400000−2i32i322-22i3−2i32i2−2i2−2i22i2−2i22i22i2−2i2000000002-2002i3−2i30000i2−i2−i2i26−6−66−i2i2i2−i2−666−600000000000000000000000000000000
χ954-4-4400-20-44000002i3−2i322-2−2i32i3−2i22i22i2−2i22i2−2i2−2i22i2000000002-200−2i32i30000−i2i2i2−i26−6−66i2−i2−i2i2−666−600000000000000000000000000000000
χ964-4-4400-20-44000002i3−2i322-2−2i32i32i2−2i2−2i22i2−2i22i22i2−2i2000000002-200−2i32i30000i2−i2−i2i2−666−6−i2i2i2−i26−6−6600000000000000000000000000000000

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