Finite Group Databasebeta

← Group #10713311

Character table — Group #10713311

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order12222234444444466666668888448888881212121212121212121212122424242424242424242424242424242444441212121212121212888888881616161616161616
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
χ91111-1-1111-1-111-1-1-1-1111-1-111111-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ101111-1-1111-1-111-1-1-1-1111-1-111111-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ111111-1-1111-1-111-1-1-1-1111-1-111111-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ121111-1-1111-1-111-1-1-1-1111-1-111111-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ131111-1-11-1-11111-1-1-1-1111-1-11111-11-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ141111-1-11-1-11111-1-1-1-1111-1-11111-11-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ151111-1-11-1-11111-1-1-1-1111-1-11111-11-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ161111-1-11-1-11111-1-1-1-1111-1-11111-11-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111
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
χ312222-2-222222-2-222-2-2222-2-20000-2-20000002222-2-2-2-222-2-2000000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ322222-2-222222-2-222-2-2222-2-20000-2-20000002222-2-2-2-222-2-2000000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ332222-2-2222-2-222-2-2-2-2222-2-2-2-2-2-22-222-2-222-2-22222-2-2-2-222-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ342222-2-22-2-22222-2-2-2-2222-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-2222222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ352222-2-22-2-2-2-2-2-222-2-2222-2-200002200000022-2-22222-2-2-2-2000000000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ362222-2-22-2-2-2-2-2-222-2-2222-2-200002200000022-2-22222-2-2-2-2000000000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ372222-2-2-122-2-222-2-211-1-1-11122222-2-2-222-2-211-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111112i−2i2i−2i−i−iii−i−iii0000000000000000
χ382222-2-2-122-2-222-2-211-1-1-11122222-2-2-222-2-211-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111−2i2i−2i2iii−i−iii−i−i0000000000000000
χ392222-2-2-122-2-222-2-211-1-1-111-2-2-2-22-222-2-22211-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-100003−3−333−3−330000000000000000
χ402222-2-2-122-2-222-2-211-1-1-111-2-2-2-22-222-2-22211-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-10000−333−3−333−30000000000000000
χ412222-2-2-1-2-22222-2-211-1-1-1112222-22-2-2-2-222111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-12i−2i−2i2i−i−iiiii−i−i0000000000000000
χ422222-2-2-1-2-22222-2-211-1-1-1112222-22-2-2-2-222111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−2i2i2i−2iii−i−i−i−iii0000000000000000
χ432222-2-2-1-2-22222-2-211-1-1-111-2-2-2-2-222222-2-2111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111100003−3−33−333−30000000000000000
χ442222-2-2-1-2-22222-2-211-1-1-111-2-2-2-2-222222-2-2111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111110000−333−33−3−330000000000000000
χ4522-2-22-2200002-22-2222-2-2-2-222-2-2002-200002-2000000002-222-2-222-2-20000000000000000000000002-22-200000000
χ4622-2-22-2200002-22-2222-2-2-2-222-2-2002-200002-2000000002-222-2-222-2-2000000000000000000000000-22-2200000000
χ4722-2-22-2200002-22-2222-2-2-2-2-2-22200-2200002-2000000002-2-2-222-2-222000000000000000000002i−2i2i−2i000000000000
χ4822-2-22-2200002-22-2222-2-2-2-2-2-22200-2200002-2000000002-2-2-222-2-22200000000000000000000−2i2i−2i2i000000000000
χ4922-2-2-22200002-2-22-2-22-2-22222-2-200-220000-22000000002-222-2-2-2-2220000000000000000000000002i−2i−2i2i00000000
χ5022-2-2-22200002-2-22-2-22-2-22222-2-200-220000-22000000002-222-2-2-2-222000000000000000000000000−2i2i2i−2i00000000
χ5122-2-2-22200002-2-22-2-22-2-222-2-222002-20000-22000000002-2-2-22222-2-2000000000000000000002-2-22000000000000
χ5222-2-2-22200002-2-22-2-22-2-222-2-222002-20000-22000000002-2-2-22222-2-200000000000000000000-222-2000000000000
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
χ554444-4-4-24444-4-44422-2-2-2220000-4-4000000-2-2-2-22222-2-22200000000000000000000000000000000000000000000
χ564444-4-4-2-4-4-4-4-4-44422-2-2-222000044000000-2-222-2-2-2-2222200000000000000000000000000000000000000000000
χ5744-4-44-440000-44-44444-4-4-4-4000000000000-4400000000-4400000000000000000000000000000000000000000000
χ5844-4-44-4-200004-44-4-2-2-2222244-4-4004-40000-2200000000-22-2-222-2-222000000000000000000000000000000000000
χ5944-4-44-4-200004-44-4-2-2-22222-4-44400-440000-2200000000-2222-2-222-2-2000000000000000000000000000000000000
χ6044-4-44-4-20000-44-44-2-2-222220000000000002-2000000002-200000000−2i3−2i32i32i3−2i3−2i32i32i30000000000000000000000000000
χ6144-4-44-4-20000-44-44-2-2-222220000000000002-2000000002-2000000002i32i3−2i3−2i32i32i3−2i3−2i30000000000000000000000000000
χ6244-4-4-4440000-444-4-4-44-4-4440000000000004-400000000-4400000000000000000000000000000000000000000000
χ6344-4-4-44-200004-4-4422-222-2-244-4-400-4400002-200000000-22-2-22222-2-2000000000000000000000000000000000000
χ6444-4-4-44-200004-4-4422-222-2-2-4-444004-400002-200000000-2222-2-2-2-222000000000000000000000000000000000000
χ6544-4-4-44-20000-444-422-222-2-2000000000000-22000000002-200000000−2i3−2i32i32i32i32i3−2i3−2i30000000000000000000000000000
χ6644-4-4-44-20000-444-422-222-2-2000000000000-22000000002-2000000002i32i3−2i3−2i3−2i3−2i32i32i30000000000000000000000000000
χ674-44-4004004-4000000-44-400−2i22i2−2i22i2000000−2i22i2000000004-400−2i22i2−2i22i200000000−2i22i2−2i22i20000000000000000000000000000
χ684-44-4004004-4000000-44-4002i2−2i22i2−2i20000002i2−2i2000000004-4002i2−2i22i2−2i2000000002i2−2i22i2−2i20000000000000000000000000000
χ694-44-400400-44000000-44-400−2i22i2−2i22i20000002i2−2i200000000-4400−2i22i2−2i22i2000000002i2−2i22i2−2i20000000000000000000000000000
χ704-44-400400-44000000-44-4002i2−2i22i2−2i2000000−2i22i200000000-44002i2−2i22i2−2i200000000−2i22i2−2i22i20000000000000000000000000000
χ714-44-400-2004-40000−2i32i32-22−2i32i3−2i22i2−2i22i2000000−2i22i20000−2i32i300-2200i2−i2i2−i26−66−66−66−6i2−i2i2−i20000000000000000000000000000
χ724-44-400-2004-40000−2i32i32-22−2i32i32i2−2i22i2−2i20000002i2−2i20000−2i32i300-2200−i2i2−i2i2−66−66−66−66−i2i2−i2i20000000000000000000000000000
χ734-44-400-2004-400002i3−2i32-222i3−2i3−2i22i2−2i22i2000000−2i22i200002i3−2i300-2200i2−i2i2−i2−66−66−66−66i2−i2i2−i20000000000000000000000000000
χ744-44-400-2004-400002i3−2i32-222i3−2i32i2−2i22i2−2i20000002i2−2i200002i3−2i300-2200−i2i2−i2i26−66−66−66−6−i2i2−i2i20000000000000000000000000000
χ754-44-400-200-440000−2i32i32-22−2i32i3−2i22i2−2i22i20000002i2−2i200002i3−2i3002-200i2−i2i2−i26−66−6−66−66−i2i2−i2i20000000000000000000000000000
χ764-44-400-200-440000−2i32i32-22−2i32i32i2−2i22i2−2i2000000−2i22i200002i3−2i3002-200−i2i2−i2i2−66−666−66−6i2−i2i2−i20000000000000000000000000000
χ774-44-400-200-4400002i3−2i32-222i3−2i3−2i22i2−2i22i20000002i2−2i20000−2i32i3002-200i2−i2i2−i2−66−666−66−6−i2i2−i2i20000000000000000000000000000
χ784-44-400-200-4400002i3−2i32-222i3−2i32i2−2i22i2−2i2000000−2i22i20000−2i32i3002-200−i2i2−i2i26−66−6−66−66i2−i2i2−i20000000000000000000000000000
χ794-4-440044-400000000-4-4400−2i22i22i2−2i20000−2i22i200004-400000000−2i22i22i2−2i20000−2i22i22i2−2i200000000000000000000000000000000
χ804-4-440044-400000000-4-44002i2−2i2−2i22i200002i2−2i200004-4000000002i2−2i2−2i22i200002i2−2i2−2i22i200000000000000000000000000000000
χ814-4-44004-4400000000-4-4400−2i22i22i2−2i200002i2−2i20000-4400000000−2i22i22i2−2i200002i2−2i2−2i22i200000000000000000000000000000000
χ824-4-44004-4400000000-4-44002i2−2i2−2i22i20000−2i22i20000-44000000002i2−2i2−2i22i20000−2i22i22i2−2i200000000000000000000000000000000
χ834-4-4400-24-4000000−2i32i322-22i3−2i3−2i22i22i2−2i20000−2i22i20000-2200−2i32i30000i2−i2−i2i26−6−66i2−i2−i2i26−6−660000000000000000000000000000
χ844-4-4400-24-4000000−2i32i322-22i3−2i32i2−2i2−2i22i200002i2−2i20000-2200−2i32i30000−i2i2i2−i2−666−6−i2i2i2−i2−666−60000000000000000000000000000
χ854-4-4400-24-40000002i3−2i322-2−2i32i3−2i22i22i2−2i20000−2i22i20000-22002i3−2i30000i2−i2−i2i2−666−6i2−i2−i2i2−666−60000000000000000000000000000
χ864-4-4400-24-40000002i3−2i322-2−2i32i32i2−2i2−2i22i200002i2−2i20000-22002i3−2i30000−i2i2i2−i26−6−66−i2i2i2−i26−6−660000000000000000000000000000
χ874-4-4400-2-44000000−2i32i322-22i3−2i3−2i22i22i2−2i200002i2−2i200002-2002i3−2i30000i2−i2−i2i26−6−66−i2i2i2−i2−666−60000000000000000000000000000
χ884-4-4400-2-44000000−2i32i322-22i3−2i32i2−2i2−2i22i20000−2i22i200002-2002i3−2i30000−i2i2i2−i2−666−6i2−i2−i2i26−6−660000000000000000000000000000
χ894-4-4400-2-440000002i3−2i322-2−2i32i3−2i22i22i2−2i200002i2−2i200002-200−2i32i30000i2−i2−i2i2−666−6−i2i2i2−i26−6−660000000000000000000000000000
χ904-4-4400-2-440000002i3−2i322-2−2i32i32i2−2i2−2i22i20000−2i22i200002-200−2i32i30000−i2i2i2−i26−6−66i2−i2−i2i2−666−60000000000000000000000000000

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