Finite Group Databasebeta

← Group #10713676

Character table — Group #10713676

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order122222344444444666666688884488888812121212121212121212121224242424242424242424242424242424222266666666888888881616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111-1-1-1-1111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111-1-1-1-1111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111-1-1-1-1111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111-1-1-1-1111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111-1-1111-1-111-1-1-1-1-1-1111-1-1-1-11-11111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1111-1-111-1-1-1-1-1-1111-1-1-1-11-11111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111-1-1111-1-111-1-1-1-1-1-1111-1-1-1-11-11111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111-1-1111-1-111-1-1-1-1-1-1111-1-1-1-11-11111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111-1-11-1-11111-1-1-1-1-1-1111-1-1-1-1-1111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111-1-11-1-11111-1-1-1-1-1-1111-1-1-1-1-1111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111-1-11-1-11111-1-1-1-1-1-1111-1-1-1-1-1111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111-1-11-1-11111-1-1-1-1-1-1111-1-1-1-1-1111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222222222222-2-2-2-222-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ18222222222-2-2-2-2-2-222222220000-22000000-2-222-2-222-2-2-2-2000000000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ19222222222-2-2-2-2-2-222222220000-22000000-2-222-2-222-2-2-2-2000000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ202222222-2-222-2-2-2-2222222200002-2000000-2-2-2-222-2-222-2-2000000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ212222222-2-222-2-2-2-2222222200002-2000000-2-2-2-222-2-222-2-2000000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ222222222-2-2-2-222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ23222222-122222222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ24222222-122222222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ25222222-122222222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ26222222-122222222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ27222222-1-2-2-2-22222-1-1-1-1-1-1-12222-2-222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111122-2-2-1-1-1-111110000000000000000
χ28222222-1-2-2-2-22222-1-1-1-1-1-1-12222-2-222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111-2-2221111-1-1-1-10000000000000000
χ29222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ30222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ312222-2-222222-2-222-2-2-2-22220000-2-20000002222-2-2-2-222-2-20000000000000000000000000000000000002−2−222−2−22
χ322222-2-222222-2-222-2-2-2-22220000-2-20000002222-2-2-2-222-2-2000000000000000000000000000000000000−222−2−222−2
χ332222-2-2222-2-222-2-2-2-2-2-222222222-2-2-2-2-222-2-22222-2-2-2-222-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ342222-2-22-2-22222-2-2-2-2-2-22222222-22-2-222-2-2-2-2-2-2-2-2222222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ352222-2-22-2-2-2-2-2-222-2-2-2-222200002200000022-2-22222-2-2-2-20000000000000000000000000000000000002−2−22−222−2
χ362222-2-22-2-2-2-2-2-222-2-2-2-222200002200000022-2-22222-2-2-2-2000000000000000000000000000000000000−222−22−2−22
χ372222-2-2-122-2-222-2-21111-1-1-122222-2-2-2-2-22211-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-10000−i3i3i3−i3−i3i3i3−i30000000000000000
χ382222-2-2-122-2-222-2-21111-1-1-122222-2-2-2-2-22211-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-10000i3−i3−i3i3i3−i3−i3i30000000000000000
χ392222-2-2-122-2-222-2-21111-1-1-1-2-2-2-22-22222-2-211-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111112-22-2-1-111-1-1110000000000000000
χ402222-2-2-122-2-222-2-21111-1-1-1-2-2-2-22-22222-2-211-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-22-2211-1-111-1-10000000000000000
χ412222-2-2-1-2-22222-2-21111-1-1-12222-22-2-222-2-2111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111110000−i3i3i3−i3i3−i3−i3i30000000000000000
χ422222-2-2-1-2-22222-2-21111-1-1-12222-22-2-222-2-2111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111110000i3−i3−i3i3−i3i3i3−i30000000000000000
χ432222-2-2-1-2-22222-2-21111-1-1-1-2-2-2-2-2222-2-222111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-12-2-22-1-11111-1-10000000000000000
χ442222-2-2-1-2-22222-2-21111-1-1-1-2-2-2-2-2222-2-222111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-222-211-1-1-1-1110000000000000000
χ4522-2-22-2200002-22-222-2-22-2-222-2-2002-200002-2000000002-222-2-222-2-20000000000000000000000002i−2i2i−2i00000000
χ4622-2-22-2200002-22-222-2-22-2-222-2-2002-200002-2000000002-222-2-222-2-2000000000000000000000000−2i2i−2i2i00000000
χ4722-2-22-2200002-22-222-2-22-2-2-2-22200-2200002-2000000002-2-2-222-2-222000000000000000000002-22-2000000000000
χ4822-2-22-2200002-22-222-2-22-2-2-2-22200-2200002-2000000002-2-2-222-2-22200000000000000000000-22-22000000000000
χ4922-2-2-22200002-2-22-2-2222-2-222-2-200-220000-22000000002-2-2-22222-2-2000000000000000000002i−2i−2i2i000000000000
χ5022-2-2-22200002-2-22-2-2222-2-222-2-200-220000-22000000002-2-2-22222-2-200000000000000000000−2i2i2i−2i000000000000
χ5122-2-2-22200002-2-22-2-2222-2-2-2-222002-20000-22000000002-222-2-2-2-2220000000000000000000000002-2-2200000000
χ5222-2-2-22200002-2-22-2-2222-2-2-2-222002-20000-22000000002-222-2-2-2-222000000000000000000000000-222-200000000
χ53444444-244-4-4-4-4-4-4-2-2-2-2-2-2-20000-4400000022-2-222-2-2222200000000000000000000000000000000000000000000
χ54444444-2-4-444-4-4-4-4-2-2-2-2-2-2-200004-40000002222-2-222-2-22200000000000000000000000000000000000000000000
χ554444-4-4-24444-4-4442222-2-2-20000-4-4000000-2-2-2-22222-2-22200000000000000000000000000000000000000000000
χ564444-4-4-2-4-4-4-4-4-4442222-2-2-2000044000000-2-222-2-2-2-2222200000000000000000000000000000000000000000000
χ5744-4-44-440000-44-4444-4-44-4-4000000000000-4400000000-4400000000000000000000000000000000000000000000
χ5844-4-44-4-200004-44-4-2-222-22244-4-4004-40000-2200000000-22-2-222-2-222000000000000000000000000000000000000
χ5944-4-44-4-200004-44-4-2-222-222-4-44400-440000-2200000000-2222-2-222-2-2000000000000000000000000000000000000
χ6044-4-44-4-20000-44-44-2-222-2220000000000002-2000000002-200000000−2i3−2i32i32i3−2i3−2i32i32i30000000000000000000000000000
χ6144-4-44-4-20000-44-44-2-222-2220000000000002-2000000002-2000000002i32i3−2i3−2i32i32i3−2i3−2i30000000000000000000000000000
χ6244-4-4-4440000-444-4-4-4444-4-40000000000004-400000000-4400000000000000000000000000000000000000000000
χ6344-4-4-44-200004-4-4422-2-2-22244-4-400-4400002-200000000-2222-2-2-2-222000000000000000000000000000000000000
χ6444-4-4-44-200004-4-4422-2-2-222-4-444004-400002-200000000-22-2-22222-2-2000000000000000000000000000000000000
χ6544-4-4-44-20000-444-422-2-2-222000000000000-22000000002-200000000−2i3−2i32i32i32i32i3−2i3−2i30000000000000000000000000000
χ6644-4-4-44-20000-444-422-2-2-222000000000000-22000000002-2000000002i32i3−2i3−2i3−2i3−2i32i32i30000000000000000000000000000
χ674-44-4004004-400000000-44-422−2222−22000022−2200000000004-400000022−2222−2222−2222−2200000000000000000000000000000000
χ684-44-4004004-400000000-44-4−2222−22220000−222200000000004-4000000−2222−2222−2222−222200000000000000000000000000000000
χ694-44-400400-4400000000-44-422−2222−220000−22220000000000-4400000022−2222−22−2222−222200000000000000000000000000000000
χ704-44-400400-4400000000-44-4−2222−2222000022−220000000000-44000000−2222−222222−2222−2200000000000000000000000000000000
χ714-44-400-2004-40000−2i32i3−2i32i32-2222−2222−22000022−22000000−2i32i300-2200i6−i6i6−i6−22−22−22−22i6−i6i6−i60000000000000000000000000000
χ724-44-400-2004-40000−2i32i3−2i32i32-22−2222−22220000−2222000000−2i32i300-2200−i6i6−i6i62−22−22−22−2−i6i6−i6i60000000000000000000000000000
χ734-44-400-2004-400002i3−2i32i3−2i32-2222−2222−22000022−220000002i3−2i300-2200−i6i6−i6i6−22−22−22−22−i6i6−i6i60000000000000000000000000000
χ744-44-400-2004-400002i3−2i32i3−2i32-22−2222−22220000−22220000002i3−2i300-2200i6−i6i6−i62−22−22−22−2i6−i6i6−i60000000000000000000000000000
χ754-44-400-200-440000−2i32i3−2i32i32-2222−2222−220000−22220000002i3−2i3002-200i6−i6i6−i6−22−222−22−2−i6i6−i6i60000000000000000000000000000
χ764-44-400-200-440000−2i32i3−2i32i32-22−2222−2222000022−220000002i3−2i3002-200−i6i6−i6i62−22−2−22−22i6−i6i6−i60000000000000000000000000000
χ774-44-400-200-4400002i3−2i32i3−2i32-2222−2222−220000−2222000000−2i32i3002-200−i6i6−i6i6−22−222−22−2i6−i6i6−i60000000000000000000000000000
χ784-44-400-200-4400002i3−2i32i3−2i32-22−2222−2222000022−22000000−2i32i3002-200i6−i6i6−i62−22−2−22−22−i6i6−i6i60000000000000000000000000000
χ794-4-440044-40000000000-4-4422−22−222200000022−22004-400000000000022−22−2222000022−22−22220000000000000000000000000000
χ804-4-440044-40000000000-4-44−222222−22000000−2222004-4000000000000−222222−220000−222222−220000000000000000000000000000
χ814-4-44004-440000000000-4-4422−22−2222000000−222200-4400000000000022−22−22220000−222222−220000000000000000000000000000
χ824-4-44004-440000000000-4-44−222222−2200000022−2200-44000000000000−222222−22000022−22−22220000000000000000000000000000
χ834-4-4400-24-4000000−2i32i32i3−2i322-222−22−222200000022−2200-2200−2i32i30000i6−i6−i6i6−222−2i6−i6−i6i6−222−20000000000000000000000000000
χ844-4-4400-24-4000000−2i32i32i3−2i322-2−222222−22000000−222200-2200−2i32i30000−i6i6i6−i62−2−22−i6i6i6−i62−2−220000000000000000000000000000
χ854-4-4400-24-40000002i3−2i3−2i32i322-222−22−222200000022−2200-22002i3−2i30000−i6i6i6−i6−222−2−i6i6i6−i6−222−20000000000000000000000000000
χ864-4-4400-24-40000002i3−2i3−2i32i322-2−222222−22000000−222200-22002i3−2i30000i6−i6−i6i62−2−22i6−i6−i6i62−2−220000000000000000000000000000
χ874-4-4400-2-44000000−2i32i32i3−2i322-222−22−2222000000−2222002-2002i3−2i30000i6−i6−i6i6−222−2−i6i6i6−i62−2−220000000000000000000000000000
χ884-4-4400-2-44000000−2i32i32i3−2i322-2−222222−2200000022−22002-2002i3−2i30000−i6i6i6−i62−2−22i6−i6−i6i6−222−20000000000000000000000000000
χ894-4-4400-2-440000002i3−2i3−2i32i322-222−22−2222000000−2222002-200−2i32i30000−i6i6i6−i6−222−2i6−i6−i6i62−2−220000000000000000000000000000
χ904-4-4400-2-440000002i3−2i3−2i32i322-2−222222−2200000022−22002-200−2i32i30000i6−i6−i6i62−2−22−i6i6i6−i6−222−20000000000000000000000000000

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