Finite Group Databasebeta

← Group #10901358

Character table — Group #10901358

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444444446666666441212121212121212444488881212121212121212121224242424242424242244444444121212124444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ9111111111-1-1-1-111111111111-1-1111-1-1-1-1111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-111-1-111-1-111-1-11-1
χ10111111111-1-1-1-111111111111-1-1111-1-1-1-1111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1111-111-1-1-1-111-1-111-11
χ11111111111-1-1-1-111111111111-1-1111-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-11-1-11111-1-1-1-111-11
χ12111111111-1-1-1-111111111111-1-1111-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11-1-111-1-11111-1-11-1
χ13111111111-1-1-1-111111111111-1-1111-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-11-1-111-1-11111-1-1-11
χ14111111111-1-1-1-111111111111-1-1111-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-11-1-11111-1-1-1-1111-1
χ15111111111-1-1-1-111111111111-1-1111-1-1-1-11-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-11-111-1-1-1-111-1-1111-1
χ16111111111-1-1-1-111111111111-1-1111-1-1-1-11-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-111-1-111-1-111-1-1-11
χ172222222222222-2-2-2-22222222-2-2-2-2-22222-200000000-2-200000000000000002222-2-2-2-20000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-2-22222-200000000-2-20000000000000000-2-2-2-222220000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000022000000000000000022-2-2-2-2220000000000000000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000220000000000000000-2-22222-2-20000000000000000
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-10000000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-222-2-211-1-1-1-11111-1-1-1-11111000000002-2-1-1110000000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2-2-22211-1-1-1-111111111-1-1-1-100000000-2211-1-10000000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-22222-2-2111111-1-1-1-1-1-1-1-1111100000000-2211-1-10000000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-222-2-222111111-1-1-1-11111-1-1-1-1000000002-2-1-1110000000000
χ2922-2-222-2-2222-2-2000022-2-2-2-220000022-2-200000−i2i2−i2i20000000000−i2−i2i2i2−i2−i2i2i22-22-200000000000000−i2i2−i2i200
χ3022-2-222-2-2222-2-2000022-2-2-2-220000022-2-200000−i2i2−i2i20000000000−i2−i2i2i2−i2−i2i2i2-22-2200000000000000i2−i2i2−i200
χ3122-2-222-2-2222-2-2000022-2-2-2-220000022-2-200000i2−i2i2−i20000000000i2i2−i2−i2i2i2−i2−i22-22-200000000000000i2−i2i2−i200
χ3222-2-222-2-2222-2-2000022-2-2-2-220000022-2-200000i2−i2i2−i20000000000i2i2−i2−i2i2i2−i2−i2-22-2200000000000000−i2i2−i2i200
χ3322-2-222-2-22-2-222000022-2-2-2-2200000-2-22200000−i2i2i2−i20000000000−i2−i2i2i2i2i2−i2−i22-2-2200000000000000−i2i2i2−i200
χ3422-2-222-2-22-2-222000022-2-2-2-2200000-2-22200000−i2i2i2−i20000000000−i2−i2i2i2i2i2−i2−i2-222-200000000000000i2−i2−i2i200
χ3522-2-222-2-22-2-222000022-2-2-2-2200000-2-22200000i2−i2−i2i20000000000i2i2−i2−i2−i2−i2i2i22-2-2200000000000000i2−i2−i2i200
χ3622-2-222-2-22-2-222000022-2-2-2-2200000-2-22200000i2−i2−i2i20000000000i2i2−i2−i2−i2−i2i2i2-222-200000000000000−i2i2i2−i200
χ372-2-2-22-22222-22-22-22-2-2-2-2-22222-22-2-22-22-222-22-200002-222-2-222-2-200000000000000000000000000000000
χ382-2-2-22-22222-22-22-22-2-2-2-2-22222-22-2-22-22-22-22-2200002-2-2-222-2-22200000000000000000000000000000000
χ392-2-2-22-22222-22-2-22-22-2-2-2-2222-22-2222-22-2-200000000-220000000000000000000000000000002-22-2000000
χ402-2-2-22-22222-22-2-22-22-2-2-2-2222-22-2222-22-2-200000000-22000000000000000000000000000000-22-22000000
χ412-2-2-22-2222-22-222-22-2-2-2-2-2222-222-2-2-22-2222-2-220000-2222-2-2-2-22200000000000000000000000000000000
χ422-2-2-22-2222-22-222-22-2-2-2-2-2222-222-2-2-22-222-222-20000-22-2-22222-2-200000000000000000000000000000000
χ432-2-2-22-2222-22-22-22-22-2-2-2-22222-2-222-22-22-2000000002-20000000000000000000000000000002-2-22000000
χ442-2-2-22-2222-22-22-22-22-2-2-2-22222-2-222-22-22-2000000002-2000000000000000000000000000000-222-2000000
χ452-2-2-22-222-12-22-22-22-21111-1-1-12-2-111-11-11-12-22-20000-11-1-111-1-111−i3i3−i3i3−i3i3−i3i30000000000−i3i3−i3i30000000000
χ462-2-2-22-222-12-22-22-22-21111-1-1-12-2-111-11-11-12-22-20000-11-1-111-1-111i3−i3i3−i3i3−i3i3−i30000000000i3−i3i3−i30000000000
χ472-2-2-22-222-12-22-22-22-21111-1-1-12-2-111-11-11-1-22-220000-1111-1-111-1-1−i3i3−i3i3−i3i3−i3i30000000000i3−i3i3−i30000000000
χ482-2-2-22-222-12-22-22-22-21111-1-1-12-2-111-11-11-1-22-220000-1111-1-111-1-1i3−i3i3−i3i3−i3i3−i30000000000−i3i3−i3i30000000000
χ492-2-2-22-222-1-22-222-22-21111-1-1-1-22-1111-11-1-12-2-2200001-1-1-11111-1-1−i3i3−i3i3i3−i3i3−i30000000000−i3i3i3−i30000000000
χ502-2-2-22-222-1-22-222-22-21111-1-1-1-22-1111-11-1-12-2-2200001-1-1-11111-1-1i3−i3i3−i3−i3i3−i3i30000000000i3−i3−i3i30000000000
χ512-2-2-22-222-1-22-222-22-21111-1-1-1-22-1111-11-1-1-222-200001-111-1-1-1-111−i3i3−i3i3i3−i3i3−i30000000000i3−i3−i3i30000000000
χ522-2-2-22-222-1-22-222-22-21111-1-1-1-22-1111-11-1-1-222-200001-111-1-1-1-111i3−i3i3−i3−i3i3−i3i30000000000−i3i3i3−i30000000000
χ5344444444-24444-4-4-4-4-2-2-2-2-2-2-2-4-4222-2-2-2-2200000000220000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2442222222200000000-2-20000000000000000000000000000000000000000
χ55444-4-4-44-44000000004-44-44-4-40000000000000000000000000000000000000000004-40000000000000000
χ56444-4-4-44-44000000004-44-44-4-4000000000000000000000000000000000000000000-440000000000000000
χ5744-44-4-4-44400004-4-444-4-44-44-40044-40000-400000000000000000000000000000000000000000000000000
χ5844-44-4-4-4440000-444-44-4-44-44-400-4-440000400000000000000000000000000000000000000000000000000
χ5944-44-4-4-44-200004-4-44-222-22-2200-2-220000200000000000000−2i32i3−2i32i300000000000000000000000000000000
χ6044-44-4-4-44-200004-4-44-222-22-2200-2-2200002000000000000002i3−2i32i3−2i300000000000000000000000000000000
χ6144-44-4-4-44-20000-444-4-222-22-220022-20000-2000000000023−2323−23000000000000000000000000000000000000
χ6244-44-4-4-44-20000-444-4-222-22-220022-20000-20000000000−2323−2323000000000000000000000000000000000000
χ6344-4-444-4-4-244-4-40000-2-22222-200000-2-22200000−2i22i2−2i22i20000000000i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ6444-4-444-4-4-244-4-40000-2-22222-200000-2-222000002i2−2i22i2−2i20000000000−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ6544-4-444-4-4-2-4-4440000-2-22222-20000022-2-200000−2i22i22i2−2i20000000000i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ6644-4-444-4-4-2-4-4440000-2-22222-20000022-2-2000002i2−2i2−2i22i20000000000−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ674-4444-4-4-444-4-440000-4-444-4-44000004-4-44000000000000000000000000000000000000000000000000000
χ684-4444-4-4-44-444-40000-4-444-4-4400000-444-4000000000000000000000000000000000000000000000000000
χ694-4444-4-4-4-24-4-44000022-2-222-200000-222-200000000000000000006−6−666−6−66000000000000000000000000
χ704-4444-4-4-4-24-4-44000022-2-222-200000-222-20000000000000000000−666−6−666−6000000000000000000000000
χ714-4444-4-4-4-2-444-4000022-2-222-2000002-2-2200000000000000000006−6−66−666−6000000000000000000000000
χ724-4444-4-4-4-2-444-4000022-2-222-2000002-2-220000000000000000000−666−66−6−66000000000000000000000000
χ734-44-4-44-444000044-4-4-444-4-44-4004-440000-400000000000000000000000000000000000000000000000000
χ744-44-4-44-4440000-4-444-444-4-44-400-44-40000400000000000000000000000000000000000000000000000000
χ754-44-4-44-44-2000044-4-42-2-222-2200-22-20000200000000000000−2i32i32i3−2i300000000000000000000000000000000
χ764-44-4-44-44-2000044-4-42-2-222-2200-22-200002000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ774-44-4-44-44-20000-4-4442-2-222-22002-220000-2000000000023−23−2323000000000000000000000000000000000000
χ784-44-4-44-44-20000-4-4442-2-222-22002-220000-20000000000−232323−23000000000000000000000000000000000000
χ794-4-44-444-4400000000-44-444-4-400000000000000000000000000000000000000004i−4i000000000000000000
χ804-4-44-444-4400000000-44-444-4-40000000000000000000000000000000000000000−4i4i000000000000000000
χ814-4-4-44-444-24-44-4-44-442222-2-2-2-442-2-2-22-222000000002-20000000000000000000000000000000000000000
χ824-4-4-44-444-2-44-44-44-442222-2-2-24-42-2-22-22-2200000000-220000000000000000000000000000000000000000
χ83888-8-8-88-8-400000000-44-44-444000000000000000000000000000000000000000000000000000000000000
χ848-8-88-888-8-4000000004-44-4-444000000000000000000000000000000000000000000000000000000000000

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