Finite Group Databasebeta

← Group #10825709

Character table — Group #10825709

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444466666666888888888888888888888888121212121616161616161616242424242424242424242424
order122222223444466666668888121212124444444444444444448812121212242424242424242488881212121212121212444444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-11111-1-1-1-1-1
χ3111111111111111111111111111111111111-1-11-1-1-1-11-1-1111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-111
χ4111111111111111111111111111111111111-1-1-1-1-111-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-111-1-1-1-1-111-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1111-1-1-1-111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111-1-111111-1-111
χ911111111111111111111-1-1-1-1111111111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1111-1-1-1-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-111-11111
χ1111111111111111111111-1-1-1-1111111111111-1-1111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-111-1-1111-1-1
χ1211111111111111111111-1-1-1-1111111111111-1-1-11111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11111-1-1-1-1-111
χ1311111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-111-1-1-11111
χ1411111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111-1-11-1-1-1-1
χ1511111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-111-1-111-1-1-111
χ1611111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1-1-111111-1-1
χ17222222222-2-2-2-222222220000-2-2-2-22222-2-2-2-20020000-2000022-2-200000000000000000000-200000020000
χ18222222222-2-2-2-222222220000-2-2-2-22222-2-2-2-200-2000020000-2-222000000000000000000002000000-20000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-222220020000-2000022-2-2000000000000000000002000000-20000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2222200-2000020000-2-22200000000000000000000-200000020000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-100000000222222222222-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-10000000022-222-2-2-2-2-2-2-21111-1-1-1-111110000-1-111-1-111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-100000000-2-22-2-2-2-22-2-222-1-1-1-1-1-1-1-1-1-1-1-1000011111111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-100000000-2-2-2-2-222-222-2-21111-1-1-1-11111000011-1-111-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-100000000222-2-2222-2-2-2-2-1-1-1-111111111000011-1-1-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000000022-2-2-2-2-2-2222211111111-1-1-1-100001111-1-1-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-100000000-2-2222-2-2222-2-2-1-1-1-1111111110000-1-11111-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-100000000-2-2-22222-2-2-22211111111-1-1-1-10000-1-1-1-11111000000000000
χ2922-22-22-2-2222-2-22-222-2-2-2000022-2-222-2-222-2-2000002-2000000000000000000000002-2000002-2000000000
χ3022-22-22-2-2222-2-22-222-2-2-2000022-2-222-2-222-2-200000-2200000000000000000000000-2200000-22000000000
χ3122-22-22-2-2222-2-22-222-2-2-2000022-2-2-2-222-2-222000002-2000000000000000000000002-200000-22000000000
χ3222-22-22-2-2222-2-22-222-2-2-2000022-2-2-2-222-2-22200000-2200000000000000000000000-22000002-2000000000
χ3322-22-22-2-22-2-2222-222-2-2-20000-2-22222-2-2-2-2222i−2i0000000000000000000000000000002i−2i00000002i−2i00000
χ3422-22-22-2-22-2-2222-222-2-2-20000-2-22222-2-2-2-222−2i2i000000000000000000000000000000−2i2i0000000−2i2i00000
χ3522-22-22-2-22-2-2222-222-2-2-20000-2-222-2-22222-2-22i−2i0000000000000000000000000000002i−2i0000000−2i2i00000
χ3622-22-22-2-22-2-2222-222-2-2-20000-2-222-2-22222-2-2−2i2i000000000000000000000000000000−2i2i00000002i−2i00000
χ372-22-2-222-222-22-2-2-22-2-22200002-2-222i−2i2i−2i2i−2i2i−2i00000000002-20000000022-2-200000000000000000000002i−2i
χ382-22-2-222-222-22-2-2-22-2-22200002-2-222i−2i2i−2i2i−2i2i−2i0000000000-2200000000-2-2220000000000000000000000−2i2i
χ392-22-2-222-222-22-2-2-22-2-22200002-2-22−2i2i−2i2i−2i2i−2i2i00000000002-20000000022-2-20000000000000000000000−2i2i
χ402-22-2-222-222-22-2-2-22-2-22200002-2-22−2i2i−2i2i−2i2i−2i2i0000000000-2200000000-2-22200000000000000000000002i−2i
χ412-22-2-222-22-22-22-2-22-2-2222i2i−2i−2i-222-22i−2i2i−2i−2i2i−2i2i00000000000000002i2i−2i−2i000022-2-200000000000000000000
χ422-22-2-222-22-22-22-2-22-2-2222i2i−2i−2i-222-2−2i2i−2i2i2i−2i2i−2i00000000000000002i2i−2i−2i0000-2-22200000000000000000000
χ432-22-2-222-22-22-22-2-22-2-222−2i−2i2i2i-222-22i−2i2i−2i−2i2i−2i2i0000000000000000−2i−2i2i2i0000-2-22200000000000000000000
χ442-22-2-222-22-22-22-2-22-2-222−2i−2i2i2i-222-2−2i2i−2i2i2i−2i2i−2i0000000000000000−2i−2i2i2i000022-2-200000000000000000000
χ452-2-2-222-2222-2-22-222-22-2-200002-22-22i−2i−2i2i2i−2i−2i2i0002-2000000000000000000000002-20000000002i−2i0000000
χ462-2-2-222-2222-2-22-222-22-2-200002-22-22i−2i−2i2i2i−2i−2i2i000-2200000000000000000000000-22000000000−2i2i0000000
χ472-2-2-222-2222-2-22-222-22-2-200002-22-2−2i2i2i−2i−2i2i2i−2i0002-2000000000000000000000002-2000000000−2i2i0000000
χ482-2-2-222-2222-2-22-222-22-2-200002-22-2−2i2i2i−2i−2i2i2i−2i000-2200000000000000000000000-220000000002i−2i0000000
χ492-2-2-222-222-222-2-222-22-2-20000-22-222i−2i−2i2i−2i2i2i−2i000000002i−2i0000000000000000000000002i−2i000000002-200
χ502-2-2-222-222-222-2-222-22-2-20000-22-222i−2i−2i2i−2i2i2i−2i00000000−2i2i000000000000000000000000−2i2i00000000-2200
χ512-2-2-222-222-222-2-222-22-2-20000-22-22−2i2i2i−2i2i−2i−2i2i000000002i−2i0000000000000000000000002i−2i00000000-2200
χ522-2-2-222-222-222-2-222-22-2-20000-22-22−2i2i2i−2i2i−2i−2i2i00000000−2i2i000000000000000000000000−2i2i000000002-200
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-200002222000000000040000-40000-2-22200000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2000022220000000000-400004000022-2-200000000000000000000000000000000
χ55444-44-4-4-4400004-4-4-444-422−2222−22000000000000000000000000000022−2222−220000000000000000000000000000
χ56444-44-4-4-4400004-4-4-444-4−2222−22220000000000000000000000000000−2222−22220000000000000000000000000000
χ57444-44-4-4-4-20000-2222-2-2222−2222−220000000000000000000000000023−23−22−226−66−6000000000000000000000000
χ58444-44-4-4-4-20000-2222-2-2222−2222−2200000000000000000000000000−2323−22−22−66−66000000000000000000000000
χ59444-44-4-4-4-20000-2222-2-22−2222−22220000000000000000000000000023−232−22−2−66−66000000000000000000000000
χ60444-44-4-4-4-20000-2222-2-22−2222−222200000000000000000000000000−23232−22−26−66−6000000000000000000000000
χ6144-44-44-4-4-244-4-4-22-2-22220000-2-22200000000000004-400000000000000000000000-220000000000000000
χ6244-44-44-4-4-244-4-4-22-2-22220000-2-2220000000000000-44000000000000000000000002-20000000000000000
χ6344-44-44-4-4-2-4-444-22-2-2222000022-2-2000000004i−4i000000000000000000000000000000−2i2i00000000000000
χ6444-44-44-4-4-2-4-444-22-2-2222000022-2-200000000−4i4i0000000000000000000000000000002i−2i00000000000000
χ6544-4-4-4-4444000044-4-4-4-440000000000000000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ6644-4-4-4-4444000044-4-4-4-4400000000000000000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ674-444-4-4-4440000-44-44-44-4−2i22i22i2−2i20000000000000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ684-444-4-4-4440000-44-44-44-42i2−2i2−2i22i200000000000000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ694-444-4-4-44-200002-22-22-22−2i22i22i2−2i2000000000000000000000000−2i32i300i2−i2−i2i26−6−66000000000000000000000000
χ704-444-4-4-44-200002-22-22-22−2i22i22i2−2i20000000000000000000000002i3−2i300i2−i2−i2i2−666−6000000000000000000000000
χ714-444-4-4-44-200002-22-22-222i2−2i2−2i22i2000000000000000000000000−2i32i300−i2i2i2−i2−666−6000000000000000000000000
χ724-444-4-4-44-200002-22-22-222i2−2i2−2i22i20000000000000000000000002i3−2i300−i2i2i2−i26−6−66000000000000000000000000
χ734-44-4-444-4-24-44-422-222-2-20000-222-20000000000000000004-400000000-2-222000000000000000000000000
χ744-44-4-444-4-24-44-422-222-2-20000-222-2000000000000000000-440000000022-2-2000000000000000000000000
χ754-44-4-444-4-2-44-4422-222-2-24i4i−4i−4i2-2-22000000000000000000000000−2i−2i2i2i0000000000000000000000000000
χ764-44-4-444-4-2-44-4422-222-2-2−4i−4i4i4i2-2-220000000000000000000000002i2i−2i−2i0000000000000000000000000000
χ774-4-444-44-440000-4-4-444-440000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ784-4-444-44-440000-4-4-444-4400000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ794-4-4-444-44-24-4-442-2-22-2220000-22-22000000000004-400000000000000000000000-22000000000000000000
χ804-4-4-444-44-24-4-442-2-22-2220000-22-2200000000000-44000000000000000000000002-2000000000000000000
χ814-4-4-444-44-2-444-42-2-22-22200002-22-200000000000000004i−4i000000000000000000000000−2i2i000000000000
χ824-4-4-444-44-2-444-42-2-22-22200002-22-20000000000000000−4i4i0000000000000000000000002i−2i000000000000
χ8388-8-8-8-888-40000-4-44444-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-88-8-40000444-4-44-40000000000000000000000000000000000000000000000000000000000000000

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