Finite Group Databasebeta

← Group #10853317

Character table — Group #10853317

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444444444444444444444448888121212121212121216161616161616161616242424242424242424242424
order122222223444444446666666448888888812121212121212121212121224242424242424242424242424242424444444444444441212121212121212224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-111-1-111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-11111
χ911111111111-1-1-1-1111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111111-111-1-111-1-1-1-1111-1-1-111-1-1
χ1011111111111-1-1-1-1111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11-111-1-111-1-111-1-1-1111-1-111
χ1111111111111-1-1-1-1111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11-1-111-1-11111-1-11-11111-1-1
χ1211111111111-1-1-1-1111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-11-1-111-1-111-1-111-11-1-1-1-111
χ1311111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1111-1-1-1-111-1-1-1-11-111-1-111
χ1411111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1111-1-1-1-1111111-11-1-111-1-1
χ1511111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11-1-1-11111-1-111111-1-1-1-1-111
χ1611111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-11111111-1-1-11111-1-1-1-1-1-1-111111-1-1
χ17222222222-2-22222-2-22222222-2-200000000-2-22222-2-2-2-2-2-2000000000000000000002222000000000000000000-2-2000000
χ18222222222-2-22222-2-22222222-2-200000000-2-22222-2-2-2-2-2-200000000000000000000-2-2-2-200000000000000000022000000
χ19222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-22222-2-20000000000000000000022-2-2000000000000000000-22000000
χ20222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-22222-2-200000000000000000000-2-2220000000000000000002-2000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000000022-1-1-1-1-1-1-1-1000000000000
χ2222222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-211111111000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111222200000000-2-2-1-1-1-11111000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-200000000221111-1-1-1-1000000000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111122-2-2000000002-2-1-111-1-111000000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111-2-22200000000-2211-1-111-1-1000000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-122-2-200000000-22-1-11111-1-1000000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-1-2-222000000002-211-1-1-1-111000000000000
χ29222-2-2-22-222222-2-2-2-2-2-2222-2-22-2000000002222-2-222-2-2-2-200000000000000000000000022-2-200000000002-20000000000
χ30222-2-2-22-222222-2-2-2-2-2-2222-2-22-2000000002222-2-222-2-2-2-2000000000000000000000000-2-2220000000000-220000000000
χ31222-2-2-22-2222-2-222-2-2-2-2222-2-2-220000000022-2-222-2-222-2-200000000000000000000000022-2-20000000000-220000000000
χ32222-2-2-22-2222-2-222-2-2-2-2222-2-2-220000000022-2-222-2-222-2-2000000000000000000000000-2-22200000000002-20000000000
χ33222-2-2-22-22-2-222-2-222-2-2222-2-2-2200000000-2-222-2-2-2-2222200000000000000002i−2i2i−2i00000000002i−2i2i−2i0000000000000000
χ34222-2-2-22-22-2-222-2-222-2-2222-2-2-2200000000-2-222-2-2-2-222220000000000000000−2i2i−2i2i0000000000−2i2i−2i2i0000000000000000
χ35222-2-2-22-22-2-2-2-22222-2-2222-2-22-200000000-2-2-2-22222-2-22200000000000000002i−2i−2i2i00000000002i−2i−2i2i0000000000000000
χ36222-2-2-22-22-2-2-2-22222-2-2222-2-22-200000000-2-2-2-22222-2-2220000000000000000−2i2i2i−2i0000000000−2i2i2i−2i0000000000000000
χ37222-2-2-22-2-1-2-222-2-22211-1-1-111-220000000011-1-11111-1-1-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i32i−2i2i−2i0000000000−ii−ii3−33−3000000000000
χ38222-2-2-22-2-1-2-222-2-22211-1-1-111-220000000011-1-11111-1-1-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−2i2i−2i2i0000000000i−ii−i−33−33000000000000
χ39222-2-2-22-2-1-2-222-2-22211-1-1-111-220000000011-1-11111-1-1-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i32i−2i2i−2i0000000000−ii−ii−33−33000000000000
χ40222-2-2-22-2-1-2-222-2-22211-1-1-111-220000000011-1-11111-1-1-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3−2i2i−2i2i0000000000i−ii−i3−33−3000000000000
χ41222-2-2-22-2-1-2-2-2-2222211-1-1-1112-2000000001111-1-1-1-111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32i−2i−2i2i0000000000−iii−i3−3−33000000000000
χ42222-2-2-22-2-1-2-2-2-2222211-1-1-1112-2000000001111-1-1-1-111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3−2i2i2i−2i0000000000i−i−ii−333−3000000000000
χ43222-2-2-22-2-1-2-2-2-2222211-1-1-1112-2000000001111-1-1-1-111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32i−2i−2i2i0000000000−iii−i−333−3000000000000
χ44222-2-2-22-2-1-2-2-2-2222211-1-1-1112-2000000001111-1-1-1-111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3−2i2i2i−2i0000000000i−i−ii3−3−33000000000000
χ4522-222-2-2-222-20000-222-22-2-22-2002i2i−2i−2i00002-2000000002-22i2i−2i−2i2i2i−2i−2i00000000000000002i−2i2i−2i0000000000002-200000000
χ4622-222-2-2-222-20000-222-22-2-22-2002i2i−2i−2i00002-2000000002-22i2i−2i−2i2i2i−2i−2i0000000000000000−2i2i−2i2i000000000000-2200000000
χ4722-222-2-2-222-20000-222-22-2-22-200−2i−2i2i2i00002-2000000002-2−2i−2i2i2i−2i−2i2i2i00000000000000002i−2i2i−2i000000000000-2200000000
χ4822-222-2-2-222-20000-222-22-2-22-200−2i−2i2i2i00002-2000000002-2−2i−2i2i2i−2i−2i2i2i0000000000000000−2i2i−2i2i0000000000002-200000000
χ4922-2-2-22-2222-200002-2-222-2-2-220000002i2i−2i−2i2-200000000-22000000002i2i−2i−2i2i2i−2i−2i000000002i−2i−2i2i00000000000000002-20000
χ5022-2-2-22-2222-200002-2-222-2-2-220000002i2i−2i−2i2-200000000-22000000002i2i−2i−2i2i2i−2i−2i00000000−2i2i2i−2i0000000000000000-220000
χ5122-2-2-22-2222-200002-2-222-2-2-22000000−2i−2i2i2i2-200000000-2200000000−2i−2i2i2i−2i−2i2i2i000000002i−2i−2i2i0000000000000000-220000
χ5222-2-2-22-2222-200002-2-222-2-2-22000000−2i−2i2i2i2-200000000-2200000000−2i−2i2i2i−2i−2i2i2i00000000−2i2i2i−2i00000000000000002-20000
χ532-2-22-222-22002-22-200-22-22-22-200−i2i2−i2i2−i2i2−i2i2002-22-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200002-22-20000000000000000000000−i2i2−i2i2
χ542-2-22-222-22002-22-200-22-22-22-200−i2i2−i2i2−i2i2−i2i2002-22-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000-22-220000000000000000000000i2−i2i2−i2
χ552-2-22-222-22002-22-200-22-22-22-200i2−i2i2−i2i2−i2i2−i2002-22-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200002-22-20000000000000000000000i2−i2i2−i2
χ562-2-22-222-22002-22-200-22-22-22-200i2−i2i2−i2i2−i2i2−i2002-22-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000-22-220000000000000000000000−i2i2−i2i2
χ572-2-22-222-2200-22-2200-22-22-22-200−i2i2−i2i2i2−i2i2−i200-22-22000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200002-2-220000000000000000000000−i2i2i2−i2
χ582-2-22-222-2200-22-2200-22-22-22-200−i2i2−i2i2i2−i2i2−i200-22-22000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000-222-20000000000000000000000i2−i2−i2i2
χ592-2-22-222-2200-22-2200-22-22-22-200i2−i2i2−i2−i2i2−i2i200-22-22000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200002-2-220000000000000000000000i2−i2−i2i2
χ602-2-22-222-2200-22-2200-22-22-22-200i2−i2i2−i2−i2i2−i2i200-22-22000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000-222-20000000000000000000000−i2i2i2−i2
χ6144444444-2-4-44444-4-4-2-2-2-2-2-2-2-4-40000000022-2-2-2-222222200000000000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24400000000222222-2-2-2-22200000000000000000000000000000000000000000000000000
χ63444-4-4-44-4-24444-4-4-4-422-2-2-2224-400000000-2-2-2-222-2-2222200000000000000000000000000000000000000000000000000
χ64444-4-4-44-4-244-4-444-4-422-2-2-222-4400000000-2-222-2-222-2-22200000000000000000000000000000000000000000000000000
χ6544-444-4-4-44-4400004-44-44-4-44-40000000000-4400000000-4400000000000000000000000000000000000000000000000000
χ6644-444-4-4-4-24-40000-44-22-222-22004i4i−4i−4i0000-2200000000-22−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000
χ6744-444-4-4-4-24-40000-44-22-222-2200−4i−4i4i4i0000-2200000000-222i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000
χ6844-444-4-4-4-2-4400004-4-22-222-2200000000002-2000000002-2000000002323−23−23−23−2323230000000000000000000000000000000000
χ6944-444-4-4-4-2-4400004-4-22-222-2200000000002-2000000002-200000000−23−2323232323−23−230000000000000000000000000000000000
χ7044-4-4-44-444-440000-44-444-4-4-440000000000-44000000004-400000000000000000000000000000000000000000000000000
χ7144-4-4-44-44-24-400004-42-2-2222-20000004i4i−4i−4i-22000000002-200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000
χ7244-4-4-44-44-24-400004-42-2-2222-2000000−4i−4i4i4i-22000000002-2000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000
χ7344-4-4-44-44-2-440000-442-2-2222-200000000002-200000000-222323−23−23−23−232323000000000000000000000000000000000000000000
χ7444-4-4-44-44-2-440000-442-2-2222-200000000002-200000000-22−23−2323232323−23−23000000000000000000000000000000000000000000
χ754-444-4-4-44400000000-4-4-4-44440022−22−2222000000000000000022−22−222222−22−2222000000000000000000000000000000000000000000
χ764-444-4-4-44400000000-4-4-4-444400−222222−220000000000000000−222222−22−222222−22000000000000000000000000000000000000000000
χ774-444-4-4-44-2000000002222-2-2-20022−22−22220000000000−2i32i3−2i32i300−222−2−222−2i6−i6−i6i6−i6i6i6−i60000000000000000000000000000000000
χ784-444-4-4-44-2000000002222-2-2-20022−22−222200000000002i3−2i32i3−2i300−222−2−222−2−i6i6i6−i6i6−i6−i6i60000000000000000000000000000000000
χ794-444-4-4-44-2000000002222-2-2-200−222222−220000000000−2i32i3−2i32i3002−2−222−2−22−i6i6i6−i6i6−i6−i6i60000000000000000000000000000000000
χ804-444-4-4-44-2000000002222-2-2-200−222222−2200000000002i3−2i32i3−2i3002−2−222−2−22i6−i6−i6i6−i6i6i6−i60000000000000000000000000000000000
χ814-44-444-4-440000000044-4-44-4-400000022−22−22220000000000000000000022−22−222222−22−22220000000000000000000000000000000000
χ824-44-444-4-440000000044-4-44-4-4000000−222222−2200000000000000000000−222222−22−222222−220000000000000000000000000000000000
χ834-44-444-4-4-200000000-2-222-22200000022−22−2222000000−2i32i32i3−2i300−i6i6i6−i6i6−i6−i6i6−222−2−222−20000000000000000000000000000000000
χ844-44-444-4-4-200000000-2-222-22200000022−22−22220000002i3−2i3−2i32i300i6−i6−i6i6−i6i6i6−i6−222−2−222−20000000000000000000000000000000000
χ854-44-444-4-4-200000000-2-222-222000000−222222−22000000−2i32i32i3−2i300i6−i6−i6i6−i6i6i6−i62−2−222−2−220000000000000000000000000000000000
χ864-44-444-4-4-200000000-2-222-222000000−222222−220000002i3−2i3−2i32i300−i6i6i6−i6i6−i6−i6i62−2−222−2−220000000000000000000000000000000000
χ874-4-44-444-4-2004-44-4002-22-22-2200−2i22i2−2i22i2−2i22i2−2i22i200-22-22000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000000000000000000000
χ884-4-44-444-4-2004-44-4002-22-22-22002i2−2i22i2−2i22i2−2i22i2−2i200-22-22000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000000000000000000000
χ894-4-44-444-4-200-44-44002-22-22-2200−2i22i2−2i22i22i2−2i22i2−2i2002-22-2000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000000000000000000000
χ904-4-44-444-4-200-44-44002-22-22-22002i2−2i22i2−2i2−2i22i2−2i22i2002-22-2000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000000000000000000000
χ914-4-4-44-4444004-4-44004-4-44-4-440000000000004-4-4400000000000000000000000000000000000000000000000000000000
χ924-4-4-44-444400-444-4004-4-44-4-44000000000000-444-400000000000000000000000000000000000000000000000000000000
χ934-4-4-44-444-2004-4-4400-222-222-2000000000000-222-20000006−66−6−66−666−66−6−66−660000000000000000000000000000000000
χ944-4-4-44-444-2004-4-4400-222-222-2000000000000-222-2000000−66−666−66−6−66−666−66−60000000000000000000000000000000000
χ954-4-4-44-444-200-444-400-222-222-20000000000002-2-220000006−66−6−66−66−66−666−66−60000000000000000000000000000000000
χ964-4-4-44-444-200-444-400-222-222-20000000000002-2-22000000−66−666−66−66−66−6−66−660000000000000000000000000000000000

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