Finite Group Databasebeta

← Group #10845409

Character table — Group #10845409

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order12222222344444444666666644121212121212121222446666888812121212121224242424242424248888888844121212122244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ911111111111-1-1-1-1111111111-1-1111-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-11-111-1-11-11-1
χ1011111111111-1-1-1-1111111111-1-1111-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-111-1-1-11-1-111-11-11
χ1111111111111-1-1-1-1111111111-1-1111-1-1-1-1111-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111-1111-1-1-11-11
χ1211111111111-1-1-1-1111111111-1-1111-1-1-1-1111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1111-1-1-1111-11-1
χ1311111111111-1-1-1-1111111111-1-1111-1-1-1-11-1-111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-1-1111-1-1-1111-1-11
χ1411111111111-1-1-1-1111111111-1-1111-1-1-1-11-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-1-111-1111-1-1-111-1
χ1511111111111-1-1-1-1111111111-1-1111-1-1-1-11-1-111-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-11-111-1-1-11-1-111-111-1
χ1611111111111-1-1-1-1111111111-1-1111-1-1-1-11-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111-111-1-11-111-1-11-1-11
χ17222222222-2-22222-2-22222222-2-2-2-2-22222-2000000000000-2-200000000000000000000000000220000-2-200
χ18222222222-2-22222-2-22222222-2-2-2-2-22222-2000000000000-2-200000000000000000000000000-2-200002200
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000000022000000000000000000000000002-20000-2200
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000000002200000000000000000000000000-2200002-200
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-11111111100000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2-1-11111111111110000000022-1-1-1-10000000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2-1-1-1-122-2-2111111-1-1-1-11111000000002-2-1-1110000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2-1-1-1-1-2-2221111111111-1-1-1-100000000-2211-1-10000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-222111122-2-211-1-1-1-1-1-1-1-1111100000000-2211-1-10000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-2221111-2-22211-1-1-1-11111-1-1-1-1000000002-2-1-1110000000000
χ2922-22-22-2-222-20000-2222-2-22-2-2002-2-200002002i−2i00000000002i2i−2i−2i00000000000022-2-2000000002i−2i000000
χ3022-22-22-2-222-20000-2222-2-22-2-2002-2-200002002i−2i00000000002i2i−2i−2i000000000000-2-22200000000−2i2i000000
χ3122-22-22-2-222-20000-2222-2-22-2-2002-2-20000200−2i2i0000000000−2i−2i2i2i00000000000022-2-200000000−2i2i000000
χ3222-22-22-2-222-20000-2222-2-22-2-2002-2-20000200−2i2i0000000000−2i−2i2i2i000000000000-2-222000000002i−2i000000
χ332-22-2-222-222222-2-2-2-2-2-2-2-22222-222-222-2-2-20000000000002-20000000000002i2i−2i−2i2i−2i2i−2i0000000000000000
χ342-22-2-222-222222-2-2-2-2-2-2-2-22222-222-222-2-2-20000000000002-2000000000000−2i−2i2i2i−2i2i−2i2i0000000000000000
χ352-22-2-222-2222-2-222-2-2-2-2-2-2222-2222-2-2-222-2000000000000-220000000000002i2i−2i−2i−2i2i−2i2i0000000000000000
χ362-22-2-222-2222-2-222-2-2-2-2-2-2222-2222-2-2-222-2000000000000-22000000000000−2i−2i2i2i2i−2i2i−2i0000000000000000
χ372-22-2-222-22-2-222-2-222-2-2-2-2222-22-2-2222-2-22000000002-22-2-22000022-2-222-2-2000000000000000000000000
χ382-22-2-222-22-2-222-2-222-2-2-2-2222-22-2-2222-2-2200000000-22-22-220000-2-222-2-222000000000000000000000000
χ392-22-2-222-22-2-2-2-22222-2-2-2-22222-2-2-22-2-2222000000002-2-222-2000022-2-2-2-222000000000000000000000000
χ402-22-2-222-22-2-2-2-22222-2-2-2-22222-2-2-22-2-222200000000-222-22-20000-2-22222-2-2000000000000000000000000
χ412-22-2-222-2-1-2-222-2-2221111-1-1-1-2211-1-1-111-10000−i3−i3i3i32-22-21-1−i3i3−i3i3-1-111-1-1110000000000−i3i3−i3i30000000000
χ422-22-2-222-2-1-2-222-2-2221111-1-1-1-2211-1-1-111-10000−i3−i3i3i3-22-221-1−i3i3−i3i311-1-111-1-10000000000i3−i3i3−i30000000000
χ432-22-2-222-2-1-2-222-2-2221111-1-1-1-2211-1-1-111-10000i3i3−i3−i32-22-21-1i3−i3i3−i3-1-111-1-1110000000000i3−i3i3−i30000000000
χ442-22-2-222-2-1-2-222-2-2221111-1-1-1-2211-1-1-111-10000i3i3−i3−i3-22-221-1i3−i3i3−i311-1-111-1-10000000000−i3i3−i3i30000000000
χ452-22-2-222-2-1-2-2-2-222221111-1-1-12-211-111-1-1-10000−i3−i3i3i32-2-22-11i3−i3i3−i3-1-11111-1-10000000000−i3i3i3−i30000000000
χ462-22-2-222-2-1-2-2-2-222221111-1-1-12-211-111-1-1-10000−i3−i3i3i3-222-2-11i3−i3i3−i311-1-1-1-1110000000000i3−i3−i3i30000000000
χ472-22-2-222-2-1-2-2-2-222221111-1-1-12-211-111-1-1-10000i3i3−i3−i32-2-22-11−i3i3−i3i3-1-11111-1-10000000000i3−i3−i3i30000000000
χ482-22-2-222-2-1-2-2-2-222221111-1-1-12-211-111-1-1-10000i3i3−i3−i3-222-2-11−i3i3−i3i311-1-1-1-1110000000000−i3i3i3−i30000000000
χ492-2-2-222-2222-200002-2-2-2222-2-2002-220000-22-2002-22-200000000000000000000002i−2i−2i2i00000000002i−2i0000
χ502-2-2-222-2222-200002-2-2-2222-2-2002-220000-22-2002-22-20000000000000000000000−2i2i2i−2i0000000000−2i2i0000
χ512-2-2-222-2222-200002-2-2-2222-2-2002-220000-2-2200-22-2200000000000000000000002i−2i−2i2i0000000000−2i2i0000
χ522-2-2-222-2222-200002-2-2-2222-2-2002-220000-2-2200-22-220000000000000000000000−2i2i2i−2i00000000002i−2i0000
χ5344444444-2-4-44444-4-4-2-2-2-2-2-2-2-4-4222-2-2-2-2200000000000022000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24422222222000000000000-2-2000000000000000000000000000000000000
χ55444-44-4-4-44000000004-44-4-44-400000000000000000000000000000000000022−2222−2200000000000000000000
χ56444-44-4-4-44000000004-44-4-44-4000000000000000000000000000000000000−2222−222200000000000000000000
χ5744-44-44-4-44-4400004-444-4-44-4-400-4440000-400000000000000000000000000000000000000000000000000
χ5844-44-44-4-4-24-40000-44-2-222-22200-2220000-2004i−4i0000000000−2i−2i2i2i00000000000000000000000000000000
χ5944-44-44-4-4-24-40000-44-2-222-22200-2220000-200−4i4i00000000002i2i−2i−2i00000000000000000000000000000000
χ6044-44-44-4-4-2-4400004-4-2-222-222002-2-2000020000−2i32i32i3−2i3000000000000000000000000000000000000000000
χ6144-44-44-4-4-2-4400004-4-2-222-222002-2-20000200002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ6244-4-4-4-4444004-44-4004-4-44-4-44000004-44-4000000000000000000000000000000000000000000000000000
χ6344-4-4-4-444400-44-44004-4-44-4-4400000-44-44000000000000000000000000000000000000000000000000000
χ6444-4-4-4-444-2004-44-400-222-222-200000-22-220000000000000000000i6−i6i6−i6i6−i6i6−i6000000000000000000000000
χ6544-4-4-4-444-2004-44-400-222-222-200000-22-220000000000000000000−i6i6−i6i6−i6i6−i6i6000000000000000000000000
χ6644-4-4-4-444-200-44-4400-222-222-2000002-22-20000000000000000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ6744-4-4-4-444-200-44-4400-222-222-2000002-22-20000000000000000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ684-444-4-4-44400000000-44-44-44-4000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ694-444-4-4-44400000000-44-44-44-40000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ704-44-4-444-4-24444-4-4-4-42222-2-2-24-4-2-22-2-2222000000000000-22000000000000000000000000000000000000
χ714-44-4-444-4-244-4-444-4-42222-2-2-2-44-2-2222-2-220000000000002-2000000000000000000000000000000000000
χ724-4-444-44-44004-4-4400-444-4-4-44000004-4-44000000000000000000000000000000000000000000000000000
χ734-4-444-44-4400-444-400-444-4-4-4400000-444-4000000000000000000000000000000000000000000000000000
χ744-4-444-44-4-2004-4-44002-2-2222-200000-222-20000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ754-4-444-44-4-2004-4-44002-2-2222-200000-222-20000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ764-4-444-44-4-200-444-4002-2-2222-2000002-2-220000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ774-4-444-44-4-200-444-4002-2-2222-2000002-2-220000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ784-4-4-444-444-440000-44-4-4444-4-400-44-40000400000000000000000000000000000000000000000000000000
χ794-4-4-444-44-24-400004-422-2-2-22200-22-2000024-400-22-22000000000000000000000000000000000000000000
χ804-4-4-444-44-24-400004-422-2-2-22200-22-200002-44002-22-2000000000000000000000000000000000000000000
χ814-4-4-444-44-2-440000-4422-2-2-222002-220000-20000000000000023−23−232300000000000000000000000000000000
χ824-4-4-444-44-2-440000-4422-2-2-222002-220000-200000000000000−232323−2300000000000000000000000000000000
χ83888-88-8-8-8-400000000-44-444-44000000000000000000000000000000000000000000000000000000000000
χ848-888-8-8-88-4000000004-44-44-44000000000000000000000000000000000000000000000000000000000000

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