Finite Group Databasebeta

← Group #10898392

Character table — Group #10898392

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444466666664444888812121212121212124444881212121212121212121224242424242424244444888844121212122244448844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-1111-1-1
χ4111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-111
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
χ7111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-1-11-1-111
χ8111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-111-111-1-1
χ911111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111-1-1-11111-1-1-1-1-1-1-11
χ1011111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-11111111-1
χ1111111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1111-1-1-1-1-111-1-1-11-1
χ1211111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1111-11
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-1-111-1-1-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1-11111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1-111-1-1-111-111-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-111111-1-11-1-11-1
χ17222222222-2-2-2-2222222222-2-200002222-2-2-2-2000000-2-2000000000000000022-2-2000000000000200-20000
χ18222222222-2-2-2-2222222222-2-200002222-2-2-2-2000000-2-20000000000000000-2-222000000000000-20020000
χ19222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-2-2-200000022000000000000000022-2-2000000000000-20020000
χ20222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-2-2-2000000220000000000000000-2-222000000000000200-20000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222221111-1-1-1-122-2-2-2-211-1-1-1-11111-1-1-1-11111000000002-211-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222221111-1-1-1-1-2-222-2-2111111-1-1-1-1-1-1-1-1111100000000-22-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-122-2-22211-1-1-1-111111111-1-1-1-100000000-22-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-1-2-22222111111-1-1-1-11111-1-1-1-1000000002-211-1-10000000000
χ29222-2-2-2-2222-22-22-2-22-2-222i−2i2i−2i00002i2i−2i−2i2-22-20000002i−2i0000000000000000000022-2-20000000000002i−2i00
χ30222-2-2-2-2222-22-22-2-22-2-222i−2i2i−2i00002i2i−2i−2i2-22-20000002i−2i00000000000000000000-2-222000000000000−2i2i00
χ31222-2-2-2-2222-22-22-2-22-2-22−2i2i−2i2i0000−2i−2i2i2i2-22-2000000−2i2i0000000000000000000022-2-2000000000000−2i2i00
χ32222-2-2-2-2222-22-22-2-22-2-22−2i2i−2i2i0000−2i−2i2i2i2-22-2000000−2i2i00000000000000000000-2-2220000000000002i−2i00
χ33222-2-2-2-222-22-222-2-22-2-222i−2i−2i2i22-2-22i2i−2i−2i-22-2200002i−2i−2i2i0000000022-2-22i2i−2i−2i000000000000000000000000
χ34222-2-2-2-222-22-222-2-22-2-222i−2i−2i2i-2-2222i2i−2i−2i-22-220000−2i2i−2i2i00000000-2-222−2i−2i2i2i000000000000000000000000
χ35222-2-2-2-222-22-222-2-22-2-22−2i2i2i−2i22-2-2−2i−2i2i2i-22-220000−2i2i2i−2i0000000022-2-2−2i−2i2i2i000000000000000000000000
χ36222-2-2-2-222-22-222-2-22-2-22−2i2i2i−2i-2-222−2i−2i2i2i-22-2200002i−2i2i−2i00000000-2-2222i2i−2i−2i000000000000000000000000
χ37222-2-2-2-22-1-22-22-111-111-12i−2i−2i2i22-2-2−i−iii1-11-100002i−2ii−i−i3−i3i3i333−3−3-1-111−i−iii00000000003−3−i3i30000000000
χ38222-2-2-2-22-1-22-22-111-111-12i−2i−2i2i22-2-2−i−iii1-11-100002i−2ii−ii3i3−i3−i3−3−333-1-111−i−iii0000000000−33i3−i30000000000
χ39222-2-2-2-22-1-22-22-111-111-12i−2i−2i2i-2-222−i−iii1-11-10000−2i2ii−i−i3−i3i3i333−3−311-1-1ii−i−i0000000000−33i3−i30000000000
χ40222-2-2-2-22-1-22-22-111-111-12i−2i−2i2i-2-222−i−iii1-11-10000−2i2ii−ii3i3−i3−i3−3−33311-1-1ii−i−i00000000003−3−i3i30000000000
χ41222-2-2-2-22-1-22-22-111-111-1−2i2i2i−2i22-2-2ii−i−i1-11-10000−2i2i−ii−i3−i3i3i3−3−333-1-111ii−i−i0000000000−33−i3i30000000000
χ42222-2-2-2-22-1-22-22-111-111-1−2i2i2i−2i22-2-2ii−i−i1-11-10000−2i2i−iii3i3−i3−i333−3−3-1-111ii−i−i00000000003−3i3−i30000000000
χ43222-2-2-2-22-1-22-22-111-111-1−2i2i2i−2i-2-222ii−i−i1-11-100002i−2i−ii−i3−i3i3i3−3−33311-1-1−i−iii00000000003−3i3−i30000000000
χ44222-2-2-2-22-1-22-22-111-111-1−2i2i2i−2i-2-222ii−i−i1-11-100002i−2i−iii3i3−i3−i333−3−311-1-1−i−iii0000000000−33−i3i30000000000
χ4522-2-2-222-222-2-22-222-2-2-220000000000002-2-22002i−2i000000002i−2i2i−2i000000002i−2i2i−2i00000000000002-200000
χ4622-2-2-222-222-2-22-222-2-2-220000000000002-2-22002i−2i000000002i−2i2i−2i00000000−2i2i−2i2i0000000000000-2200000
χ4722-2-2-222-222-2-22-222-2-2-220000000000002-2-2200−2i2i00000000−2i2i−2i2i000000002i−2i2i−2i0000000000000-2200000
χ4822-2-2-222-222-2-22-222-2-2-220000000000002-2-2200−2i2i00000000−2i2i−2i2i00000000−2i2i−2i2i00000000000002-200000
χ4922-2-2-222-22-222-2-222-2-2-22000000000000-222-22i−2i0000002i−2i2i−2i0000000000002i−2i−2i2i00000000002-200000000
χ5022-2-2-222-22-222-2-222-2-2-22000000000000-222-22i−2i0000002i−2i2i−2i000000000000−2i2i2i−2i0000000000-2200000000
χ5122-2-2-222-22-222-2-222-2-2-22000000000000-222-2−2i2i000000−2i2i−2i2i0000000000002i−2i−2i2i0000000000-2200000000
χ5222-2-2-222-22-222-2-222-2-2-22000000000000-222-2−2i2i000000−2i2i−2i2i000000000000−2i2i2i−2i00000000002-200000000
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
χ55444-4-4-4-44-24-44-4-222-222-24i−4i4i−4i0000−2i−2i2i2i-22-22000000−2i2i0000000000000000000000000000000000000000
χ56444-4-4-4-44-24-44-4-222-222-2−4i4i−4i4i00002i2i−2i−2i-22-220000002i−2i0000000000000000000000000000000000000000
χ5744-444-4-4-4444-4-4-4-4-4-444400000000000044-4-4000000000000000000000000000000000000000000000000
χ5844-444-4-4-44-4-444-4-4-4-4444000000000000-4-444000000000000000000000000000000000000000000000000
χ5944-444-4-4-4-244-4-42222-2-2-2000000000000-2-2220000000023−23−2323000000000000000000000000000000000000
χ6044-444-4-4-4-244-4-42222-2-2-2000000000000-2-22200000000−232323−23000000000000000000000000000000000000
χ6144-444-4-4-4-2-4-4442222-2-2-200000000000022-2-2000000000000−2i32i32i3−2i300000000000000000000000000000000
χ6244-444-4-4-4-2-4-4442222-2-2-200000000000022-2-20000000000002i3−2i3−2i32i300000000000000000000000000000000
χ6344-4-4-444-4-24-4-442-2-2222-2000000000000-222-2004i−4i00000000−2i2i−2i2i00000000000000000000000000000000
χ6444-4-4-444-4-24-4-442-2-2222-2000000000000-222-200−4i4i000000002i−2i2i−2i00000000000000000000000000000000
χ6544-4-4-444-4-2-444-42-2-2222-20000000000002-2-224i−4i000000−2i2i−2i2i000000000000000000000000000000000000
χ6644-4-4-444-4-2-444-42-2-2222-20000000000002-2-22−4i4i0000002i−2i2i−2i000000000000000000000000000000000000
χ674-444-44-4-440000-44-444-4-40000−2i22i2−2i22i2000000000000000000000000−2i22i2−2i22i20000000000000000000000000000
χ684-444-44-4-440000-44-444-4-400002i2−2i22i2−2i20000000000000000000000002i2−2i22i2−2i20000000000000000000000000000
χ694-444-44-4-4-200002-22-2-2220000−2i22i2−2i22i2−2i32i3−2i32i300000000000000000000i2−i2i2−i26−66−6000000000000000000000000
χ704-444-44-4-4-200002-22-2-2220000−2i22i2−2i22i22i3−2i32i3−2i300000000000000000000i2−i2i2−i2−66−66000000000000000000000000
χ714-444-44-4-4-200002-22-2-22200002i2−2i22i2−2i2−2i32i3−2i32i300000000000000000000−i2i2−i2i2−66−66000000000000000000000000
χ724-444-44-4-4-200002-22-2-22200002i2−2i22i2−2i22i3−2i32i3−2i300000000000000000000−i2i2−i2i26−66−6000000000000000000000000
χ734-44-44-44-440000-4-444-44-40000−2i22i22i2−2i2000000000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ744-44-44-44-440000-4-444-44-400002i2−2i2−2i22i20000000000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ754-44-44-44-4-2000022-2-22-220000−2i22i22i2−2i223−23−232300000000000000000000i2−i2−i2i2i6−i6−i6i6000000000000000000000000
χ764-44-44-44-4-2000022-2-22-220000−2i22i22i2−2i2−232323−2300000000000000000000i2−i2−i2i2−i6i6i6−i6000000000000000000000000
χ774-44-44-44-4-2000022-2-22-2200002i2−2i2−2i22i223−23−232300000000000000000000−i2i2i2−i2−i6i6i6−i6000000000000000000000000
χ784-44-44-44-4-2000022-2-22-2200002i2−2i2−2i22i2−232323−2300000000000000000000−i2i2i2−i2i6−i6−i6i6000000000000000000000000
χ794-4-44-4-444400004-44-44-4-400000000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ804-4-44-4-444400004-44-44-4-4000000000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ814-4-4-444-444000044-4-4-44-400000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ824-4-4-444-444000044-4-4-44-4000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ838-8-88-8-888-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-888-88-40000-4-4444-440000000000000000000000000000000000000000000000000000000000000000

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