Finite Group Databasebeta

← Group #10823173

Character table — Group #10823173

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444466666666888888888888888888888888121212121616161616161616242424242424242424242424
order1222222234444666666688881212121222224444224444444488121212122424242424242424888866121212121212222244444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1
χ3111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
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
χ61111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ911111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111
χ1111111111111111111111-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ1211111111111111111111-1-1-1-1111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-1
χ1311111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-11111
χ1411111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1111111-1-1
χ1511111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1111111-1-1-1-1-1-1
χ1611111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-111
χ17222222222-2-2-2-222222220000-2-2-2-22222-2-2-2-200002-200000022-2-20000000000000000000000002-2000000
χ18222222222-2-2-2-222222220000-2-2-2-22222-2-2-2-20000-22000000-2-222000000000000000000000000-22000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2222200002-200000022-2-2000000000000000000000000-22000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-222220000-22000000-2-2220000000000000000000000002-2000000
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
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-10000000022-2-2-2-2-2-222-2-21111-1-1-1-111110000-1-1-1-11111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-100000000-2-222-2-222-2-2-2-21111-1-1-1-1111100001111-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-100000000-2-2-2-222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1000011111111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-100000000222222-2-2-2-2-2-2-1-1-1-1111111110000-1-111-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000000022-2-2-2-222-2-22211111111-1-1-1-10000-1-11111-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-100000000-2-222-2-2-2-2222211111111-1-1-1-1000011-1-1-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-100000000-2-2-2-2222222-2-2-1-1-1-111111111000011-1-111-1-1000000000000
χ2922-2-2-22-22222-2-22-2-2-22-22000022-2-222-2-222-2-2002i−2i00000000000000000000000000002i−2i000000002i−2i0000
χ3022-2-2-22-22222-2-22-2-2-22-22000022-2-222-2-222-2-200−2i2i0000000000000000000000000000−2i2i00000000−2i2i0000
χ3122-2-2-22-22222-2-22-2-2-22-22000022-2-2-2-222-2-222002i−2i00000000000000000000000000002i−2i00000000−2i2i0000
χ3222-2-2-22-22222-2-22-2-2-22-22000022-2-2-2-222-2-22200−2i2i0000000000000000000000000000−2i2i000000002i−2i0000
χ3322-2-2-22-222-2-2222-2-2-22-220000-2-22222-2-2-2-2222-2000000000000000000000000002-20000002-20000000000
χ3422-2-2-22-222-2-2222-2-2-22-220000-2-22222-2-2-2-222-2200000000000000000000000000-22000000-220000000000
χ3522-2-2-22-222-2-2222-2-2-22-220000-2-222-2-22222-2-22-2000000000000000000000000002-2000000-220000000000
χ3622-2-2-22-222-2-2222-2-2-22-220000-2-222-2-22222-2-2-2200000000000000000000000000-220000002-20000000000
χ372-22-2-222-222-22-2-22-2-2-22200002-22-22-22-22-22-2000000002i−2i000000000000000000002i−2i0000000000002i−2i00
χ382-22-2-222-222-22-2-22-2-2-22200002-22-22-22-22-22-200000000−2i2i00000000000000000000−2i2i000000000000−2i2i00
χ392-22-2-222-222-22-2-22-2-2-22200002-22-2-22-22-22-22000000002i−2i000000000000000000002i−2i000000000000−2i2i00
χ402-22-2-222-222-22-2-22-2-2-22200002-22-2-22-22-22-2200000000−2i2i00000000000000000000−2i2i0000000000002i−2i00
χ412-22-2-222-22-22-22-22-2-2-2220000-22-222-22-2-22-220000002-2000000000000000000000000002-2002-200000000
χ422-22-2-222-22-22-22-22-2-2-2220000-22-222-22-2-22-22000000-2200000000000000000000000000-2200-2200000000
χ432-22-2-222-22-22-22-22-2-2-2220000-22-22-22-222-22-20000002-2000000000000000000000000002-200-2200000000
χ442-22-2-222-22-22-22-22-2-2-2220000-22-22-22-222-22-2000000-2200000000000000000000000000-22002-200000000
χ452-2-2222-2-222-2-22-2-222-2-2200002-2-222-2-222-2-2200000000002-20000000022-2-200000000000000000000002-2
χ462-2-2222-2-222-2-22-2-222-2-2200002-2-222-2-222-2-220000000000-2200000000-2-2220000000000000000000000-22
χ472-2-2222-2-222-2-22-2-222-2-2200002-2-22-222-2-222-200000000002-20000000022-2-20000000000000000000000-22
χ482-2-2222-2-222-2-22-2-222-2-2200002-2-22-222-2-222-20000000000-2200000000-2-22200000000000000000000002-2
χ492-2-2222-2-22-222-2-2-222-2-222i2i−2i−2i-222-22-2-22-222-200000000000000002i2i−2i−2i00002i2i−2i−2i00000000000000000000
χ502-2-2222-2-22-222-2-2-222-2-222i2i−2i−2i-222-2-222-22-2-2200000000000000002i2i−2i−2i0000−2i−2i2i2i00000000000000000000
χ512-2-2222-2-22-222-2-2-222-2-22−2i−2i2i2i-222-22-2-22-222-20000000000000000−2i−2i2i2i0000−2i−2i2i2i00000000000000000000
χ522-2-2222-2-22-222-2-2-222-2-22−2i−2i2i2i-222-2-222-22-2-220000000000000000−2i−2i2i2i00002i2i−2i−2i00000000000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2000022220000000000004-4000000-2-22200000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-200002222000000000000-4400000022-2-200000000000000000000000000000000
χ554444-4-4-4-4400004-44-4-44-4−2i22i2−2i22i20000000000000000000000000000−2i22i2−2i22i20000000000000000000000000000
χ564444-4-4-4-4400004-44-4-44-42i2−2i22i2−2i200000000000000000000000000002i2−2i22i2−2i20000000000000000000000000000
χ574444-4-4-4-4-20000-22-222-22−2i22i2−2i22i2000000000000000000000000−2i32i300i2−i2i2−i26−66−6000000000000000000000000
χ584444-4-4-4-4-20000-22-222-22−2i22i2−2i22i20000000000000000000000002i3−2i300i2−i2i2−i2−66−66000000000000000000000000
χ594444-4-4-4-4-20000-22-222-222i2−2i22i2−2i2000000000000000000000000−2i32i300−i2i2−i2i2−66−66000000000000000000000000
χ604444-4-4-4-4-20000-22-222-222i2−2i22i2−2i20000000000000000000000002i3−2i300−i2i2−i2i26−66−6000000000000000000000000
χ6144-4-44-44-44000044-44-4-4-40000000000000000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ6244-4-44-44-44000044-44-4-4-400000000000000000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ6344-4-4-44-44-244-4-4-2222-22-20000-2-22200000000004i−4i0000000000000000000000000000−2i2i00000000000000
χ6444-4-4-44-44-244-4-4-2222-22-20000-2-2220000000000−4i4i00000000000000000000000000002i−2i00000000000000
χ6544-4-4-44-44-2-4-444-2222-22-2000022-2-2000000004-400000000000000000000000000-22000000000000000000
χ6644-4-4-44-44-2-4-444-2222-22-2000022-2-200000000-44000000000000000000000000002-2000000000000000000
χ674-44-44-4-4440000-4-4-4444-4000000000000000000000000000000000000000022−22−222200000000000000000000
χ684-44-44-4-4440000-4-4-4444-40000000000000000000000000000000000000000−222222−2200000000000000000000
χ694-44-4-444-4-24-44-42-2222-2-20000-22-2200000000000000004i−4i00000000000000000000−2i2i0000000000000000
χ704-44-4-444-4-24-44-42-2222-2-20000-22-220000000000000000−4i4i000000000000000000002i−2i0000000000000000
χ714-44-4-444-4-2-44-442-2222-2-200002-22-2000000000000004-400000000000000000000000000-22000000000000
χ724-44-4-444-4-2-44-442-2222-2-200002-22-200000000000000-44000000000000000000000000002-2000000000000
χ734-4-4444-4-4-24-4-4422-2-222-20000-222-20000000000000000004-400000000-2-222000000000000000000000000
χ744-4-4444-4-4-24-4-4422-2-222-20000-222-2000000000000000000-440000000022-2-2000000000000000000000000
χ754-4-4444-4-4-2-444-422-2-222-24i4i−4i−4i2-2-22000000000000000000000000−2i−2i2i2i0000000000000000000000000000
χ764-4-4444-4-4-2-444-422-2-222-2−4i−4i4i4i2-2-220000000000000000000000002i2i−2i−2i0000000000000000000000000000
χ774-4-44-4-44440000-444-44-4-422−22−2222000000000000000000000000000022−22−22220000000000000000000000000000
χ784-4-44-4-44440000-444-44-4-4−222222−220000000000000000000000000000−222222−220000000000000000000000000000
χ794-4-44-4-444-200002-2-22-22222−22−22220000000000000000000000000023−23−222−26−6−66000000000000000000000000
χ804-4-44-4-444-200002-2-22-22222−22−222200000000000000000000000000−2323−222−2−666−6000000000000000000000000
χ814-4-44-4-444-200002-2-22-222−222222−220000000000000000000000000023−232−2−22−666−6000000000000000000000000
χ824-4-44-4-444-200002-2-22-222−222222−2200000000000000000000000000−23232−2−226−6−66000000000000000000000000
χ8388-8-88-88-8-40000-4-44-44440000000000000000000000000000000000000000000000000000000000000000
χ848-88-88-8-88-40000444-4-4-440000000000000000000000000000000000000000000000000000000000000000

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