Finite Group Databasebeta

← Group #10694651

Character table — Group #10694651

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order122222344444444666666688888888448888121212121212121212121212242424242424242424242424242424248888888888888888444412121212121212128888
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
χ51111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91111-1-11-111-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-111-1-1i−ii−i
χ101111-1-11-111-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111-1-111−ii−ii
χ111111-1-11-111-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-111-1-1−ii−ii
χ121111-1-11-111-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111-1-111i−ii−i
χ131111-1-11-111-1-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111i−i−ii
χ141111-1-11-111-1-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-111-1-1-11111-1-1−iii−i
χ151111-1-11-111-1-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111−iii−i
χ161111-1-11-111-1-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-11111-1-1i−i−ii
χ172222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ182222222222-2-2-2-222222222-2-2-2-22222-2-222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ192222222-2-2-222-2-2-22222222000000002-2000022-2-222-2-2-2-2-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ202222222-2-2-222-2-2-22222222000000002-2000022-2-222-2-2-2-2-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ212222222-2-2-2-2-222-2222222200000000-220000-2-222-2-222-2-2-2-200000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ222222222-2-2-2-2-222-2222222200000000-220000-2-222-2-222-2-2-2-20000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
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
χ25222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ26222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ27222222-1222-2-2-2-22-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-22211111111-1-1-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ28222222-1222-2-2-2-22-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-22211111111-1-1-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ29222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-2-2-22222-2-222-2-211111111-1-1-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ30222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-2-2-22222-2-222-2-211111111-1-1-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ312222-2-222-2-222-2-22-2-2-2-222200000000-220000-2-22222-2-222-2-2000000000000000022-2-2-2-222000000000000000000000000
χ322222-2-222-2-222-2-22-2-2-2-222200000000-220000-2-22222-2-222-2-20000000000000000-2-22222-2-2000000000000000000000000
χ332222-2-222-2-2-2-2222-2-2-2-2222000000002-2000022-2-2-2-22222-2-200000000000000000000000022-2-2-2-2220000000000000000
χ342222-2-222-2-2-2-2222-2-2-2-2222000000002-2000022-2-2-2-22222-2-2000000000000000000000000-2-22222-2-20000000000000000
χ352222-2-22-2222222-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-22222-2-2222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ362222-2-22-2222222-2-2-2-2-2222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ372222-2-2-1-2222222-21111-1-1-122222222-2-2-2-2-2-21111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ382222-2-2-1-2222222-21111-1-1-122222222-2-2-2-2-2-21111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ392222-2-2-1-2222222-21111-1-1-1-2-2-2-2-2-2-2-2-2-222221111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ402222-2-2-1-2222222-21111-1-1-1-2-2-2-2-2-2-2-2-2-222221111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111100000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ412222-2-2-1-222-2-2-2-2-21111-1-1-12222-2-2-2-22222-2-2-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111100000000000000002-22-2-1-111-1-1110000
χ422222-2-2-1-222-2-2-2-2-21111-1-1-12222-2-2-2-22222-2-2-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111110000000000000000-22-2211-1-111-1-10000
χ432222-2-2-1-222-2-2-2-2-21111-1-1-1-2-2-2-2222222-2-222-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-100000000000000002-2-22-1-11111-1-10000
χ442222-2-2-1-222-2-2-2-2-21111-1-1-1-2-2-2-2222222-2-222-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-10000000000000000-222-211-1-1-1-1110000
χ452-2-222-2222-20000-222-2-2-2-22000022-2-2002-200000000002-22-2000022-2-2000022-2-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ462-2-222-2222-20000-222-2-2-2-22000022-2-2002-200000000002-22-2000022-2-2000022-2-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ472-2-222-2222-20000-222-2-2-2-220000-2-22200-2200000000002-22-20000-2-2220000-2-222−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ482-2-222-2222-20000-222-2-2-2-220000-2-22200-2200000000002-22-20000-2-2220000-2-222i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ492-2-222-22-2-220000222-2-2-2-2222-2-2000000002-200000000-22-2222-2-2000022-2-200002−2−222−2−222−2−222−2−220000000000000000
χ502-2-222-22-2-220000222-2-2-2-2222-2-2000000002-200000000-22-2222-2-2000022-2-20000−222−2−222−2−222−2−222−20000000000000000
χ512-2-222-22-2-220000222-2-2-2-22-2-22200000000-2200000000-22-22-2-2220000-2-22200002−2−222−2−22−222−2−222−20000000000000000
χ522-2-222-22-2-220000222-2-2-2-22-2-22200000000-2200000000-22-22-2-2220000-2-2220000−222−2−222−22−2−222−2−220000000000000000
χ532-2-22-2222-220000-2-2-222-2-2222-2-200000000-22000000002-2-2222-2-20000-2-2220000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ542-2-22-2222-220000-2-2-222-2-2222-2-200000000-22000000002-2-2222-2-20000-2-2220000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ552-2-22-2222-220000-2-2-222-2-22-2-222000000002-2000000002-2-22-2-222000022-2-20000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ562-2-22-2222-220000-2-2-222-2-22-2-222000000002-2000000002-2-22-2-222000022-2-20000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ572-2-22-222-22-200002-2-222-2-22000022-2-200-220000000000-222-20000-2-222000022-2-22−22−2−22−22−22−222−22−20000000000000000
χ582-2-22-222-22-200002-2-222-2-22000022-2-200-220000000000-222-20000-2-222000022-2-2−22−222−22−22−22−2−22−220000000000000000
χ592-2-22-222-22-200002-2-222-2-220000-2-222002-20000000000-222-2000022-2-20000-2-2222−22−2−22−222−22−2−22−220000000000000000
χ602-2-22-222-22-200002-2-222-2-220000-2-222002-20000000000-222-2000022-2-20000-2-222−22−222−22−2−22−222−22−20000000000000000
χ61444444-2-4-4-444-4-4-4-2-2-2-2-2-2-2000000004-40000-2-222-2-2222222000000000000000000000000000000000000000000000000
χ62444444-2-4-4-4-4-444-4-2-2-2-2-2-2-200000000-44000022-2-222-2-22222000000000000000000000000000000000000000000000000
χ634444-4-4-24-4-444-4-442222-2-2-200000000-44000022-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ644444-4-4-24-4-4-4-44442222-2-2-2000000004-40000-2-22222-2-2-2-222000000000000000000000000000000000000000000000000
χ6544-4-4004000004-4000004-4-422−2222−2222−2222−220000000000004-4000022−2222−220000000022−2222−2200000000000000000000000000000000
χ6644-4-4004000004-4000004-4-4−2222−2222−2222−22220000000000004-40000−2222−222200000000−2222−222200000000000000000000000000000000
χ6744-4-400400000-44000004-4-422−2222−22−2222−2222000000000000-44000022−2222−2200000000−2222−222200000000000000000000000000000000
χ6844-4-400400000-44000004-4-4−2222−222222−2222−22000000000000-440000−2222−22220000000022−2222−2200000000000000000000000000000000
χ6944-4-400-2000004-40−2i32i3−2i32i3-22222−2222−2222−2222−2200000000−2i32i300-220000−22−22i6−i6i6−i6i6−i6i6−i6−22−2200000000000000000000000000000000
χ7044-4-400-2000004-40−2i32i3−2i32i3-222−2222−2222−2222−222200000000−2i32i300-2200002−22−2−i6i6−i6i6−i6i6−i6i62−22−200000000000000000000000000000000
χ7144-4-400-2000004-402i3−2i32i3−2i3-22222−2222−2222−2222−22000000002i3−2i300-220000−22−22−i6i6−i6i6−i6i6−i6i6−22−2200000000000000000000000000000000
χ7244-4-400-2000004-402i3−2i32i3−2i3-222−2222−2222−2222−2222000000002i3−2i300-2200002−22−2i6−i6i6−i6i6−i6i6−i62−22−200000000000000000000000000000000
χ7344-4-400-200000-440−2i32i3−2i32i3-22222−2222−22−2222−2222000000002i3−2i3002-20000−22−22−i6i6−i6i6i6−i6i6−i62−22−200000000000000000000000000000000
χ7444-4-400-200000-440−2i32i3−2i32i3-222−2222−222222−2222−22000000002i3−2i3002-200002−22−2i6−i6i6−i6−i6i6−i6i6−22−2200000000000000000000000000000000
χ7544-4-400-200000-4402i3−2i32i3−2i3-22222−2222−22−2222−222200000000−2i32i3002-20000−22−22i6−i6i6−i6−i6i6−i6i62−22−200000000000000000000000000000000
χ7644-4-400-200000-4402i3−2i32i3−2i3-222−2222−222222−2222−2200000000−2i32i3002-200002−22−2−i6i6−i6i6i6−i6i6−i6−22−2200000000000000000000000000000000
χ774-44-40040004-40000000-44-422−22−222222−22−222200000000004-400000022−22−22220000000022−22−222200000000000000000000000000000000
χ784-44-40040004-40000000-44-4−222222−22−222222−2200000000004-4000000−222222−2200000000−222222−2200000000000000000000000000000000
χ794-44-4004000-440000000-44-422−22−2222−222222−220000000000-4400000022−22−222200000000−222222−2200000000000000000000000000000000
χ804-44-4004000-440000000-44-4−222222−2222−22−22220000000000-44000000−222222−220000000022−22−222200000000000000000000000000000000
χ814-44-400-20004-4000−2i32i32i3−2i32-2222−22−222222−22−2222000000−2i32i300-22000000−222−2i6−i6−i6i6i6−i6−i6i6−222−200000000000000000000000000000000
χ824-44-400-20004-4000−2i32i32i3−2i32-22−222222−22−222222−22000000−2i32i300-220000002−2−22−i6i6i6−i6−i6i6i6−i62−2−2200000000000000000000000000000000
χ834-44-400-20004-40002i3−2i3−2i32i32-2222−22−222222−22−22220000002i3−2i300-22000000−222−2−i6i6i6−i6−i6i6i6−i6−222−200000000000000000000000000000000
χ844-44-400-20004-40002i3−2i3−2i32i32-22−222222−22−222222−220000002i3−2i300-220000002−2−22i6−i6−i6i6i6−i6−i6i62−2−2200000000000000000000000000000000
χ854-44-400-2000-44000−2i32i32i3−2i32-2222−22−2222−222222−220000002i3−2i3002-2000000−222−2−i6i6i6−i6i6−i6−i6i62−2−2200000000000000000000000000000000
χ864-44-400-2000-44000−2i32i32i3−2i32-22−222222−2222−22−22220000002i3−2i3002-20000002−2−22i6−i6−i6i6−i6i6i6−i6−222−200000000000000000000000000000000
χ874-44-400-2000-440002i3−2i3−2i32i32-2222−22−2222−222222−22000000−2i32i3002-2000000−222−2i6−i6−i6i6−i6i6i6−i62−2−2200000000000000000000000000000000
χ884-44-400-2000-440002i3−2i3−2i32i32-22−222222−2222−22−2222000000−2i32i3002-20000002−2−22−i6i6i6−i6i6−i6−i6i6−222−200000000000000000000000000000000
χ894-4-444-4-244-40000-4-2-22222-2000044-4-4004-40000000000-22-220000-2-2220000-2-22200000000000000000000000000000000
χ904-4-444-4-244-40000-4-2-22222-20000-4-44400-440000000000-22-22000022-2-2000022-2-200000000000000000000000000000000
χ914-4-444-4-2-4-4400004-2-22222-244-4-4000000004-4000000002-22-2-2-2220000-2-222000000000000000000000000000000000000
χ924-4-444-4-2-4-4400004-2-22222-2-4-44400000000-44000000002-22-222-2-2000022-2-2000000000000000000000000000000000000
χ934-4-44-44-24-440000-422-2-222-244-4-400000000-4400000000-222-2-2-222000022-2-2000000000000000000000000000000000000
χ944-4-44-44-24-440000-422-2-222-2-4-444000000004-400000000-222-222-2-20000-2-222000000000000000000000000000000000000
χ954-4-44-44-2-44-40000422-2-222-2000044-4-400-4400000000002-2-22000022-2-20000-2-22200000000000000000000000000000000
χ964-4-44-44-2-44-40000422-2-222-20000-4-444004-400000000002-2-220000-2-222000022-2-200000000000000000000000000000000

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