Finite Group Databasebeta

← Group #10823416

Character table — Group #10823416

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444466666666888888888888888888888888121212121616161616161616242424242424242424242424
order12222222344446666666224412121212444444442244444466888812122424242424242424444466121212121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
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
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111111111111111-1-1-1-111111111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-111
χ1111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-1111111111111-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1
χ1311111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111
χ1411111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-111-1-1
χ1611111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-111
χ17222222222-2-2-2-2222222222-2-2-2-2-2-22222-2-2-2-200000000220000-2-20000000022-2-200000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2222200000000220000-2-200000000-2-22200000000000000000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-22222-2-2-2-200000000-2-200002200000000-2-22200000000000000000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2222200000000-2-20000220000000022-2-200000000000000000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-10000000022222222-1-12222-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1000000002222-2-2-2-2-1-1-2-2-2-2-1-1111111110000-1-1-1-11111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-100000000-2-2-2-22222-1-1-2-2-2-2-1-11111111100001111-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-100000000-2-2-2-2-2-2-2-2-1-12222-1-1-1-1-1-1-1-1-1-1000011111111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000000022-2-222-2-21122-2-211-1-1-1-111110000-1-11111-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000000022-2-2-2-22211-2-222111111-1-1-1-10000-1-111-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-100000000-2-22222-2-211-2-222111111-1-1-1-1000011-1-111-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-100000000-2-222-2-2221122-2-211-1-1-1-11111000011-1-1-1-111000000000000
χ2922-22-2-22-222-22-22-2-2-22-2200002-22-22i2i−2i−2i2i2i−2i−2i002-2000000000000000000000000002-200002i−2i0000000000
χ3022-22-2-22-222-22-22-2-2-22-2200002-22-22i2i−2i−2i2i2i−2i−2i00-2200000000000000000000000000-220000−2i2i0000000000
χ3122-22-2-22-222-22-22-2-2-22-2200002-22-2−2i−2i2i2i−2i−2i2i2i002-2000000000000000000000000002-20000−2i2i0000000000
χ3222-22-2-22-222-22-22-2-2-22-2200002-22-2−2i−2i2i2i−2i−2i2i2i00-2200000000000000000000000000-2200002i−2i0000000000
χ3322-22-2-22-22-22-222-2-2-22-220000-22-222i2i−2i−2i−2i−2i2i2i2-2000000000000000000000000002-200000000002i−2i000000
χ3422-22-2-22-22-22-222-2-2-22-220000-22-222i2i−2i−2i−2i−2i2i2i-2200000000000000000000000000-220000000000−2i2i000000
χ3522-22-2-22-22-22-222-2-2-22-220000-22-22−2i−2i2i2i2i2i−2i−2i2-2000000000000000000000000002-20000000000−2i2i000000
χ3622-22-2-22-22-22-222-2-2-22-220000-22-22−2i−2i2i2i2i2i−2i−2i-2200000000000000000000000000-2200000000002i−2i000000
χ372-22-22-22-2222-2-2-222-2-2-220000-2-2222i−2i2i−2i2i−2i2i−2i00000000002-2000022-2-20000000000000000000000002i−2i00
χ382-22-22-22-2222-2-2-222-2-2-220000-2-2222i−2i2i−2i2i−2i2i−2i0000000000-220000-2-222000000000000000000000000−2i2i00
χ392-22-22-22-2222-2-2-222-2-2-220000-2-222−2i2i−2i2i−2i2i−2i2i00000000002-2000022-2-2000000000000000000000000−2i2i00
χ402-22-22-22-2222-2-2-222-2-2-220000-2-222−2i2i−2i2i−2i2i−2i2i0000000000-220000-2-2220000000000000000000000002i−2i00
χ412-22-22-22-22-2-222-222-2-2-22000022-2-22i−2i2i−2i−2i2i−2i2i0000000000002i−2i0000002i2i−2i−2i00000000000000000000002-2
χ422-22-22-22-22-2-222-222-2-2-22000022-2-22i−2i2i−2i−2i2i−2i2i000000000000−2i2i000000−2i−2i2i2i0000000000000000000000-22
χ432-22-22-22-22-2-222-222-2-2-22000022-2-2−2i2i−2i2i2i−2i2i−2i0000000000002i−2i0000002i2i−2i−2i0000000000000000000000-22
χ442-22-22-22-22-2-222-222-2-2-22000022-2-2−2i2i−2i2i2i−2i2i−2i000000000000−2i2i000000−2i−2i2i2i00000000000000000000002-2
χ452-2-2-2-222222-2-22-2-2-22-2220000-222-22-2-222-2-220000002-20000000000000000000000002-200002-200000000
χ462-2-2-2-222222-2-22-2-2-22-2220000-222-22-2-222-2-22000000-22000000000000000000000000-220000-2200000000
χ472-2-2-2-222222-2-22-2-2-22-2220000-222-2-222-2-222-20000002-20000000000000000000000002-20000-2200000000
χ482-2-2-2-222222-2-22-2-2-22-2220000-222-2-222-2-222-2000000-22000000000000000000000000-2200002-200000000
χ492-2-2-2-22222-222-2-2-2-22-22200002-2-222-2-22-222-200002-200000000000000000000000000002-20000002-20000
χ502-2-2-2-22222-222-2-2-2-22-22200002-2-222-2-22-222-20000-220000000000000000000000000000-22000000-220000
χ512-2-2-2-22222-222-2-2-2-22-22200002-2-22-222-22-2-2200002-200000000000000000000000000002-2000000-220000
χ522-2-2-2-22222-222-2-2-2-22-22200002-2-22-222-22-2-220000-220000000000000000000000000000-220000002-20000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-422220000000000000000-2-200002200000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44422220000000000000000220000-2-200000000000000000000000000000000
χ55444-4-4-4-444000044-4-4-44-4004i−4i000000000000000000000000004i−4i00000000000000000000000000000000
χ56444-4-4-4-444000044-4-4-44-400−4i4i00000000000000000000000000−4i4i00000000000000000000000000000000
χ57444-4-4-4-44-20000-2-2222-22004i−4i00000000000000000000000000−2i2i6−66−6i6−i6i6−i6000000000000000000000000
χ58444-4-4-4-44-20000-2-2222-22004i−4i00000000000000000000000000−2i2i−66−66−i6i6−i6i6000000000000000000000000
χ59444-4-4-4-44-20000-2-2222-2200−4i4i000000000000000000000000002i−2i6−66−6−i6i6−i6i6000000000000000000000000
χ60444-4-4-4-44-20000-2-2222-2200−4i4i000000000000000000000000002i−2i−66−66i6−i6i6−i6000000000000000000000000
χ6144-44-4-44-4-24-44-4-2222-22-20000-22-2200000000004-400000000000000000000000000-220000000000000000
χ6244-44-4-44-4-24-44-4-2222-22-20000-22-220000000000-44000000000000000000000000002-20000000000000000
χ6344-44-4-44-4-2-44-44-2222-22-200002-22-2000000004-400000000000000000000000000-22000000000000000000
χ6444-44-4-44-4-2-44-44-2222-22-200002-22-200000000-44000000000000000000000000002-2000000000000000000
χ6544-4-444-4-4400004-444-4-4-400000000000000000000000000000000000000004-40000000000000000000000
χ6644-4-444-4-4400004-444-4-4-40000000000000000000000000000000000000000-440000000000000000000000
χ674-444-44-4-440000-44-444-4-44-400000000000000000000004-400000000000000000000000000000000000000
χ684-444-44-4-440000-44-444-4-4-440000000000000000000000-4400000000000000000000000000000000000000
χ694-444-44-4-4-200002-22-2-2224-40000000000000000000000-220000006−6−666−6−66000000000000000000000000
χ704-444-44-4-4-200002-22-2-2224-40000000000000000000000-22000000−666−6−666−6000000000000000000000000
χ714-444-44-4-4-200002-22-2-222-4400000000000000000000002-20000006−6−66−666−6000000000000000000000000
χ724-444-44-4-4-200002-22-2-222-4400000000000000000000002-2000000−666−66−6−66000000000000000000000000
χ734-44-44-44-4-244-4-42-2-2222-2000022-2-20000000000000000004-40000-2-2220000000000000000000000000000
χ744-44-44-44-4-244-4-42-2-2222-2000022-2-2000000000000000000-44000022-2-20000000000000000000000000000
χ754-44-44-44-4-2-4-4442-2-2222-20000-2-222000000000000000000004i−4i000000−2i−2i2i2i000000000000000000000000
χ764-44-44-44-4-2-4-4442-2-2222-20000-2-22200000000000000000000−4i4i0000002i2i−2i−2i000000000000000000000000
χ774-4-444-4-4440000-4-44-444-40000000000000000000000000000000000000000004-400000000000000000000
χ784-4-444-4-4440000-4-44-444-4000000000000000000000000000000000000000000-4400000000000000000000
χ794-4-4-4-4444-24-4-44222-22-2-200002-2-22000000000000004-4000000000000000000000000-2200000000000000
χ804-4-4-4-4444-24-4-44222-22-2-200002-2-2200000000000000-440000000000000000000000002-200000000000000
χ814-4-4-4-4444-2-444-4222-22-2-20000-222-20000000000004-40000000000000000000000000000-22000000000000
χ824-4-4-4-4444-2-444-4222-22-2-20000-222-2000000000000-4400000000000000000000000000002-2000000000000
χ8388-8-888-8-8-40000-44-4-44440000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-8-88-4000044-44-4-440000000000000000000000000000000000000000000000000000000000000000

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