Finite Group Databasebeta

← Group #10823489

Character table — Group #10823489

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444466666666888888888888888888888888121212121616161616161616242424242424242424242424
order1222222234444666666688881212121244444444244444444466881212242424242424242488881212121212121212222244444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-11-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111
χ3111111111111111111111111111111111111-111-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ61111111111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ911111111111111111111-1-1-1-11111111111111111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-1
χ1011111111111111111111-1-1-1-11111111111111-1-1111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111-1-1111-1-1
χ1111111111111111111111-1-1-1-1111111111111-111-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-111-1-1-111
χ1211111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111
χ1311111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-11111
χ1411111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-111-1-1-111
χ1511111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-111-1-1-1-1-1-11111111111-1-1-1-11111-1-11-1-1111-1-1
χ1611111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-11111-1-1-1-1111111-1-1-1-1
χ17222222222-2-2-2-222222220000-2-2-2-22222-2-2-2-2200-20000002200-2-2000000000000000000000000-20020000
χ18222222222-2-2-2-222222220000-2-2-2-22222-2-2-2-2-2002000000-2-20022000000000000000000000000200-20000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-22222200-20000002200-2-2000000000000000000000000200-20000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-22222-2002000000-2-20022000000000000000000000000-20020000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-1000000002222222222-1-122-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1000000002-2-22-2-2-2-2-2-2-1-122-1-1-1-1-1-1-1-1-1-1000011111111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-100000000-222-222-2-2-2-211-2-211-1-1-1-111110000-1-1-1-11111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-100000000-2-2-2-2-2-2222211-2-211-1-1-1-1111100001111-1-1-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1000000002222-2-222-2-2-1-1-2-2-1-1111111110000-1-111-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1000000002-2-2222-2-222-1-1-2-2-1-111111111000011-1-111-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-100000000-222-2-2-2-2-2221122111111-1-1-1-10000-1-11111-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-100000000-2-2-2-22222-2-21122111111-1-1-1-1000011-1-1-1-111000000000000
χ2922-222-2-2-2222-2-22-2-2-222-222-2-2-2-2222i2i−2i−2i2i2i−2i−2i000000000000000022-2-200002i2i−2i−2i00000000000000000000
χ3022-222-2-2-2222-2-22-2-2-222-222-2-2-2-222−2i−2i2i2i−2i−2i2i2i000000000000000022-2-20000−2i−2i2i2i00000000000000000000
χ3122-222-2-2-2222-2-22-2-2-222-2-2-222-2-2222i2i−2i−2i2i2i−2i−2i0000000000000000-2-2220000−2i−2i2i2i00000000000000000000
χ3222-222-2-2-2222-2-22-2-2-222-2-2-222-2-222−2i−2i2i2i−2i−2i2i2i0000000000000000-2-22200002i2i−2i−2i00000000000000000000
χ3322-222-2-2-22-2-2222-2-2-222-2000022-2-22i2i−2i−2i−2i−2i2i2i0000000000002i−2i0000002i2i−2i−2i00000000000000000000002-2
χ3422-222-2-2-22-2-2222-2-2-222-2000022-2-22i2i−2i−2i−2i−2i2i2i000000000000−2i2i000000−2i−2i2i2i0000000000000000000000-22
χ3522-222-2-2-22-2-2222-2-2-222-2000022-2-2−2i−2i2i2i2i2i−2i−2i0000000000002i−2i0000002i2i−2i−2i0000000000000000000000-22
χ3622-222-2-2-22-2-2222-2-2-222-2000022-2-2−2i−2i2i2i2i2i−2i−2i000000000000−2i2i000000−2i−2i2i2i00000000000000000000002-2
χ372-22-222-2-222-22-2-222-2-22-200002-22-22i−2i2i−2i2i−2i2i−2i0000002i−2i0000000000000000000000002i−2i002-20000000000
χ382-22-222-2-222-22-2-222-2-22-200002-22-22i−2i2i−2i2i−2i2i−2i000000−2i2i000000000000000000000000−2i2i00-220000000000
χ392-22-222-2-222-22-2-222-2-22-200002-22-2−2i2i−2i2i−2i2i−2i2i0000002i−2i0000000000000000000000002i−2i00-220000000000
χ402-22-222-2-222-22-2-222-2-22-200002-22-2−2i2i−2i2i−2i2i−2i2i000000−2i2i000000000000000000000000−2i2i002-20000000000
χ412-22-222-2-22-22-22-222-2-22-20000-22-222i−2i2i−2i−2i2i−2i2i02i−2i00000000000000000000000002i−2i000000000002-200000
χ422-22-222-2-22-22-22-222-2-22-20000-22-222i−2i2i−2i−2i2i−2i2i0−2i2i0000000000000000000000000−2i2i00000000000-2200000
χ432-22-222-2-22-22-22-222-2-22-20000-22-22−2i2i−2i2i2i−2i2i−2i02i−2i00000000000000000000000002i−2i00000000000-2200000
χ442-22-222-2-22-22-22-222-2-22-20000-22-22−2i2i−2i2i2i−2i2i−2i0−2i2i0000000000000000000000000−2i2i000000000002-200000
χ452-2-2-22-22222-2-22-2-2-22-2220000-222-22-2-222-2-22000000002-20000000000000000000000002-2002-200000000
χ462-2-2-22-22222-2-22-2-2-22-2220000-222-22-2-222-2-2200000000-22000000000000000000000000-2200-2200000000
χ472-2-2-22-22222-2-22-2-2-22-2220000-222-2-222-2-222-2000000002-20000000000000000000000002-200-2200000000
χ482-2-2-22-22222-2-22-2-2-22-2220000-222-2-222-2-222-200000000-22000000000000000000000000-22002-200000000
χ492-2-2-22-2222-222-2-2-2-22-22200002-2-222-2-22-222-200002-20000000000000000000000002-20000000000002-200
χ502-2-2-22-2222-222-2-2-2-22-22200002-2-222-2-22-222-20000-22000000000000000000000000-22000000000000-2200
χ512-2-2-22-2222-222-2-2-2-22-22200002-2-22-222-22-2-2200002-20000000000000000000000002-2000000000000-2200
χ522-2-2-22-2222-222-2-2-2-22-22200002-2-22-222-22-2-220000-22000000000000000000000000-220000000000002-200
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-20000222200000000400-4000000-2-2002200000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000222200000000-40040000002200-2-200000000000000000000000000000000
χ55444-4-4-44-44000044-44-4-4-422−2222−22000000000000000000000000000022−2222−220000000000000000000000000000
χ56444-4-4-44-44000044-44-4-4-4−2222−22220000000000000000000000000000−2222−22220000000000000000000000000000
χ57444-4-4-44-4-20000-2-22-222222−2222−220000000000000000000000−2i32i30000−22−22i6−i6i6−i6000000000000000000000000
χ58444-4-4-44-4-20000-2-22-222222−2222−2200000000000000000000002i3−2i30000−22−22−i6i6−i6i6000000000000000000000000
χ59444-4-4-44-4-20000-2-22-2222−2222−22220000000000000000000000−2i32i300002−22−2−i6i6−i6i6000000000000000000000000
χ60444-4-4-44-4-20000-2-22-2222−2222−222200000000000000000000002i3−2i300002−22−2i6−i6i6−i6000000000000000000000000
χ6144-444-4-4-4-244-4-4-2222-2-2244-4-422-2-2000000000000000000000000-2-2220000000000000000000000000000
χ6244-444-4-4-4-244-4-4-2222-2-22-4-44422-2-200000000000000000000000022-2-20000000000000000000000000000
χ6344-444-4-4-4-2-4-444-2222-2-220000-2-222000000000000000000004i−4i000000−2i−2i2i2i000000000000000000000000
χ6444-444-4-4-4-2-4-444-2222-2-220000-2-22200000000000000000000−4i4i0000002i2i−2i−2i000000000000000000000000
χ6544-4-4-44-44400004-44-4-4-4422−22−2222000000000000000000000000000022−22−22220000000000000000000000000000
χ6644-4-4-44-44400004-44-4-4-44−222222−220000000000000000000000000000−222222−220000000000000000000000000000
χ6744-4-4-44-44-20000-22-2222-222−22−22220000000000000000000000000023−23−222−26−6−66000000000000000000000000
χ6844-4-4-44-44-20000-22-2222-222−22−222200000000000000000000000000−2323−222−2−666−6000000000000000000000000
χ6944-4-4-44-44-20000-22-2222-2−222222−220000000000000000000000000023−232−2−22−666−6000000000000000000000000
χ7044-4-4-44-44-20000-22-2222-2−222222−2200000000000000000000000000−23232−2−226−6−66000000000000000000000000
χ714-444-4-4-4440000-44-4-44-44000000000000000000000000000000000000000022−2222−2200000000000000000000
χ724-444-4-4-4440000-44-4-44-440000000000000000000000000000000000000000−2222−222200000000000000000000
χ734-44-444-4-4-24-44-42-2-222-220000-22-22000000000000004i−4i000000000000000000000000−2i2i00000000000000
χ744-44-444-4-4-24-44-42-2-222-220000-22-2200000000000000−4i4i0000000000000000000000002i−2i00000000000000
χ754-44-444-4-4-2-44-442-2-222-2200002-22-20000000004i−4i0000000000000000000000000−2i2i000000000000000000
χ764-44-444-4-4-2-44-442-2-222-2200002-22-2000000000−4i4i00000000000000000000000002i−2i000000000000000000
χ774-4-44-444-440000-4-4444-4-40000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ784-4-44-444-440000-4-4444-4-400000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ794-4-4-44-444-24-4-44222-22-2-200002-2-2200000000000000004-4000000000000000000000000-22000000000000
χ804-4-4-44-444-24-4-44222-22-2-200002-2-220000000000000000-440000000000000000000000002-2000000000000
χ814-4-4-44-444-2-444-4222-22-2-20000-222-20000000000004-4000000000000000000000000-220000000000000000
χ824-4-4-44-444-2-444-4222-22-2-20000-222-2000000000000-440000000000000000000000002-20000000000000000
χ838-888-8-8-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-888-8-4000044-4-4-4440000000000000000000000000000000000000000000000000000000000000000

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