Finite Group Databasebeta

← Group #10848862

Character table — Group #10848862

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121212121216161616161624242424242424244848
order1222222234444666666644448888121212121212121244448812121212121212121212242424242424242444448888246612122224448824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11-1-11-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111
χ5111111111111111111111111-1-1-1-1111111111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111-1-1-1-1111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-11-1-1-1-111
χ8111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-11111-1-1
χ911111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-11-1-111-111-1-1-1-1-1-11
χ1011111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1111111-1
χ1111111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111-111-1-1-1-1-1-111-1-11-1
χ1211111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11111-1-111-11
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11-111-1-1-111-1-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-111-1-11-1-1111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1-111-1-1-1-11111-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-1-1111111-1-1-1-11-1
χ17222222222-2-2-2-2222222222-2-200002222-2-2-2-2000000-2-2000000000000000022-2-20000000000-2002000000
χ18222222222-2-2-2-2222222222-2-200002222-2-2-2-2000000-2-20000000000000000-2-2220000000000200-2000000
χ19222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-2-2-200000022000000000000000022-2-20000000000200-2000000
χ20222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-2-2-2000000220000000000000000-2-2220000000000-2002000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-2-2-2-222-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-12222-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222221111-1-1-1-122-2-2-2-211-1-1-1-11111-1-1-1-1111100000000-2211-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222221111-1-1-1-1-2-222-2-2111111-1-1-1-1-1-1-1-11111000000002-2-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-122-2-22211-1-1-1-111111111-1-1-1-1000000002-2-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-1-2-22222111111-1-1-1-11111-1-1-1-100000000-2211-1-10000000000
χ29222-2-22-2-222-22-222-2-2-22-22i−2i2i−2i00002i2i−2i−2i2-22-20000002i−2i000000000000000000002i2i−2i−2i0000000000002-200
χ30222-2-22-2-222-22-222-2-2-22-22i−2i2i−2i00002i2i−2i−2i2-22-20000002i−2i00000000000000000000−2i−2i2i2i000000000000-2200
χ31222-2-22-2-222-22-222-2-2-22-2−2i2i−2i2i0000−2i−2i2i2i2-22-2000000−2i2i000000000000000000002i2i−2i−2i000000000000-2200
χ32222-2-22-2-222-22-222-2-2-22-2−2i2i−2i2i0000−2i−2i2i2i2-22-2000000−2i2i00000000000000000000−2i−2i2i2i0000000000002-200
χ33222-2-22-2-22-22-2222-2-2-22-22i−2i−2i2i2i2i−2i−2i2i2i−2i−2i-22-2200002-2−2i2i000000002i2i−2i−2i22-2-2000000000000000000000000
χ34222-2-22-2-22-22-2222-2-2-22-22i−2i−2i2i−2i−2i2i2i2i2i−2i−2i-22-220000-22−2i2i00000000−2i−2i2i2i-2-222000000000000000000000000
χ35222-2-22-2-22-22-2222-2-2-22-2−2i2i2i−2i2i2i−2i−2i−2i−2i2i2i-22-220000-222i−2i000000002i2i−2i−2i-2-222000000000000000000000000
χ36222-2-22-2-22-22-2222-2-2-22-2−2i2i2i−2i−2i−2i2i2i−2i−2i2i2i-22-2200002-22i−2i00000000−2i−2i2i2i22-2-2000000000000000000000000
χ37222-2-22-2-2-1-22-22-1-1111-112i−2i−2i2i2i2i−2i−2i−i−iii1-11-100002-2i−i−i3−i3i3i333−3−3−i−iii-1-1110000000000−i3i33−30000000000
χ38222-2-22-2-2-1-22-22-1-1111-112i−2i−2i2i2i2i−2i−2i−i−iii1-11-100002-2i−ii3i3−i3−i3−3−333−i−iii-1-1110000000000i3−i3−330000000000
χ39222-2-22-2-2-1-22-22-1-1111-112i−2i−2i2i−2i−2i2i2i−i−iii1-11-10000-22i−i−i3−i3i3i333−3−3ii−i−i11-1-10000000000i3−i3−330000000000
χ40222-2-22-2-2-1-22-22-1-1111-112i−2i−2i2i−2i−2i2i2i−i−iii1-11-10000-22i−ii3i3−i3−i3−3−333ii−i−i11-1-10000000000−i3i33−30000000000
χ41222-2-22-2-2-1-22-22-1-1111-11−2i2i2i−2i2i2i−2i−2iii−i−i1-11-10000-22−ii−i3−i3i3i3−3−333−i−iii11-1-10000000000i3−i33−30000000000
χ42222-2-22-2-2-1-22-22-1-1111-11−2i2i2i−2i2i2i−2i−2iii−i−i1-11-10000-22−iii3i3−i3−i333−3−3−i−iii11-1-10000000000−i3i3−330000000000
χ43222-2-22-2-2-1-22-22-1-1111-11−2i2i2i−2i−2i−2i2i2iii−i−i1-11-100002-2−ii−i3−i3i3i3−3−333ii−i−i-1-1110000000000−i3i3−330000000000
χ44222-2-22-2-2-1-22-22-1-1111-11−2i2i2i−2i−2i−2i2i2iii−i−i1-11-100002-2−iii3i3−i3−i333−3−3ii−i−i-1-1110000000000i3−i33−30000000000
χ452-2-2-222-2222-2-22-2-2-22-222000000000000-222-2002-2000000002-22-2000000002-22-2000000000000002-20000
χ462-2-2-222-2222-2-22-2-2-22-222000000000000-222-2002-2000000002-22-200000000-22-2200000000000000-220000
χ472-2-2-222-2222-2-22-2-2-22-222000000000000-222-200-2200000000-22-22000000002-22-200000000000000-220000
χ482-2-2-222-2222-2-22-2-2-22-222000000000000-222-200-2200000000-22-2200000000-22-22000000000000002-20000
χ492-2-2-222-222-222-2-2-2-22-2220000000000002-2-222-20000002-22-20000000000002-2-22000000000002-20000000
χ502-2-2-222-222-222-2-2-2-22-2220000000000002-2-222-20000002-22-2000000000000-222-200000000000-220000000
χ512-2-2-222-222-222-2-2-2-22-2220000000000002-2-22-22000000-22-220000000000002-2-2200000000000-220000000
χ522-2-2-222-222-222-2-2-2-22-2220000000000002-2-22-22000000-22-22000000000000-222-2000000000002-20000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-40000-2-2-2-22222000000220000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444000022222222000000-2-20000000000000000000000000000000000000000
χ55444-4-44-4-4-24-44-4-2-2222-224i−4i4i−4i0000−2i−2i2i2i-22-22000000−2i2i0000000000000000000000000000000000000000
χ56444-4-44-4-4-24-44-4-2-2222-22−4i4i−4i4i00002i2i−2i−2i-22-220000002i−2i0000000000000000000000000000000000000000
χ5744-444-4-4-4400004-4-444-4-40000−2i22i2−2i22i2000000000000000000000000−2i22i2−2i22i20000000000000000000000000000
χ5844-444-4-4-4400004-4-444-4-400002i2−2i22i2−2i20000000000000000000000002i2−2i22i2−2i20000000000000000000000000000
χ5944-444-4-4-4-20000-222-2-2220000−2i22i2−2i22i2−2i32i3−2i32i300000000000000000000i2−i2i2−i26−66−6000000000000000000000000
χ6044-444-4-4-4-20000-222-2-2220000−2i22i2−2i22i22i3−2i32i3−2i300000000000000000000i2−i2i2−i2−66−66000000000000000000000000
χ6144-444-4-4-4-20000-222-2-22200002i2−2i22i2−2i2−2i32i3−2i32i300000000000000000000−i2i2−i2i2−66−66000000000000000000000000
χ6244-444-4-4-4-20000-222-2-22200002i2−2i22i2−2i22i3−2i32i3−2i300000000000000000000−i2i2−i2i26−66−6000000000000000000000000
χ6344-4-4-4-444400004-44-4-4-44000022−22−222200000000000000000000000022−22−22220000000000000000000000000000
χ6444-4-4-4-444400004-44-4-4-440000−222222−22000000000000000000000000−222222−220000000000000000000000000000
χ6544-4-4-4-444-20000-22-2222-2000022−22−222223−23−232300000000000000000000−222−26−6−66000000000000000000000000
χ6644-4-4-4-444-20000-22-2222-2000022−22−2222−232323−2300000000000000000000−222−2−666−6000000000000000000000000
χ6744-4-4-4-444-20000-22-2222-20000−222222−2223−23−2323000000000000000000002−2−22−666−6000000000000000000000000
χ6844-4-4-4-444-20000-22-2222-20000−222222−22−232323−23000000000000000000002−2−226−6−66000000000000000000000000
χ694-444-4-4-4440000-44-4-44-440000000000000000000000000000000000000000000022−2222−220000000000000000
χ704-444-4-4-4440000-44-4-44-4400000000000000000000000000000000000000000000−2222−22220000000000000000
χ714-44-44-44-440000-4444-4-4-400000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ724-44-44-44-440000-4444-4-4-4000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ734-4-44-444-4444-4-4-4-44-444-4000000000000-4-444000000000000000000000000000000000000000000000000
χ744-4-44-444-44-4-444-4-44-444-400000000000044-4-4000000000000000000000000000000000000000000000000
χ754-4-44-444-4-244-4-422-22-2-2200000000000022-2-200000000−2i32i32i3−2i3000000000000000000000000000000000000
χ764-4-44-444-4-244-4-422-22-2-2200000000000022-2-2000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ774-4-44-444-4-2-4-44422-22-2-22000000000000-2-22200000000000023−23−232300000000000000000000000000000000
χ784-4-44-444-4-2-4-44422-22-2-22000000000000-2-222000000000000−232323−2300000000000000000000000000000000
χ794-4-4-444-44-24-4-44222-22-2-20000000000002-2-22004-400000000-22-2200000000000000000000000000000000
χ804-4-4-444-44-24-4-44222-22-2-20000000000002-2-2200-44000000002-22-200000000000000000000000000000000
χ814-4-4-444-44-2-444-4222-22-2-2000000000000-222-24-4000000-22-22000000000000000000000000000000000000
χ824-4-4-444-44-2-444-4222-22-2-2000000000000-222-2-440000002-22-2000000000000000000000000000000000000
χ838-888-8-8-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000
χ848-88-88-88-8-400004-4-4-44440000000000000000000000000000000000000000000000000000000000000000

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