Finite Group Databasebeta

← Group #10823186

Character table — Group #10823186

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444466666666888888888888888888888888121212121616161616161616242424242424242424242424
order12222222344446666666444412121212222244442222444488881212121224242424242424244444666612121212224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1-1-1-1-1
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
χ61111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1111111
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
χ911111111111111111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111
χ1111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111
χ1211111111111111111111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1
χ1311111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-111-1-1
χ1511111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1111111-1-1
χ1611111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111
χ17222222222-2-2-2-2222222222-2-2-2-2-2-22222-2-2-2-200000000000022-2-20000000022-2-200000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2222200000000000022-2-200000000-2-22200000000000000000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-22222-2-2-2-2000000000000-2-22200000000-2-22200000000000000000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-22222000000000000-2-2220000000022-2-200000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-10000000022-2-222-2-2-2-2-2-2-1-1-1-1111111110000-1-111-1-111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-100000000-2-222-2-222-2-2-2-2-1-1-1-111111111000011-1-111-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-100000000-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1000011111111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1000000002222-2-2-2-222-2-21111-1-1-1-111110000-1-1-1-11111000000000000
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
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-100000000-2-22222-2-2-2-22211111111-1-1-1-1000011-1-1-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-100000000-2-2-2-2222222-2-21111-1-1-1-1111100001111-1-1-1-1000000000000
χ2922-2-2-2-222222-2-22-22-2-22-2000022-2-222-2-222-2-200002i−2i000000000000000000000000002i−2i00002i−2i00000000
χ3022-2-2-2-222222-2-22-22-2-22-2000022-2-222-2-222-2-20000−2i2i00000000000000000000000000−2i2i0000−2i2i00000000
χ3122-2-2-2-222222-2-22-22-2-22-2000022-2-2-2-222-2-22200002i−2i000000000000000000000000002i−2i0000−2i2i00000000
χ3222-2-2-2-222222-2-22-22-2-22-2000022-2-2-2-222-2-2220000−2i2i00000000000000000000000000−2i2i00002i−2i00000000
χ3322-2-2-2-2222-2-2222-22-2-22-20000-2-22222-2-2-2-2222-2000000000000000000000000002-20000000000002-20000
χ3422-2-2-2-2222-2-2222-22-2-22-20000-2-22222-2-2-2-222-2200000000000000000000000000-22000000000000-220000
χ3522-2-2-2-2222-2-2222-22-2-22-20000-2-222-2-22222-2-22-2000000000000000000000000002-2000000000000-220000
χ3622-2-2-2-2222-2-2222-22-2-22-20000-2-222-2-22222-2-2-2200000000000000000000000000-220000000000002-20000
χ372-22-2-22-2222-22-2-222-2-2-2200002-22-22-22-22-22-20000002i−2i000000000000000000000000002i−2i00002i−2i000000
χ382-22-2-22-2222-22-2-222-2-2-2200002-22-22-22-22-22-2000000−2i2i00000000000000000000000000−2i2i0000−2i2i000000
χ392-22-2-22-2222-22-2-222-2-2-2200002-22-2-22-22-22-220000002i−2i000000000000000000000000002i−2i0000−2i2i000000
χ402-22-2-22-2222-22-2-222-2-2-2200002-22-2-22-22-22-22000000−2i2i00000000000000000000000000−2i2i00002i−2i000000
χ412-22-2-22-222-22-22-222-2-2-220000-22-222-22-2-22-22002-2000000000000000000000000002-200002-20000000000
χ422-22-2-22-222-22-22-222-2-2-220000-22-222-22-2-22-2200-2200000000000000000000000000-220000-220000000000
χ432-22-2-22-222-22-22-222-2-2-220000-22-22-22-222-22-2002-2000000000000000000000000002-20000-220000000000
χ442-22-2-22-222-22-22-222-2-2-220000-22-22-22-222-22-200-2200000000000000000000000000-2200002-20000000000
χ452-2-222-2-2222-2-22-2-2222-2-200002-2-222-2-222-2-22000000002-200000022-2-20000000000000000000000002-200
χ462-2-222-2-2222-2-22-2-2222-2-200002-2-222-2-222-2-2200000000-22000000-2-222000000000000000000000000-2200
χ472-2-222-2-2222-2-22-2-2222-2-200002-2-22-222-2-222-2000000002-200000022-2-2000000000000000000000000-2200
χ482-2-222-2-2222-2-22-2-2222-2-200002-2-22-222-2-222-200000000-22000000-2-2220000000000000000000000002-200
χ492-2-222-2-222-222-2-2-2222-2-20000-222-22-2-22-222-200000000002i−2i000000002i2i−2i−2i00000000000000000000002i−2i
χ502-2-222-2-222-222-2-2-2222-2-20000-222-22-2-22-222-20000000000−2i2i00000000−2i−2i2i2i0000000000000000000000−2i2i
χ512-2-222-2-222-222-2-2-2222-2-20000-222-2-222-22-2-2200000000002i−2i000000002i2i−2i−2i0000000000000000000000−2i2i
χ522-2-222-2-222-222-2-2-2222-2-20000-222-2-222-22-2-220000000000−2i2i00000000−2i−2i2i2i00000000000000000000002i−2i
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4222200000000000000000000-2-22200000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44422220000000000000000000022-2-200000000000000000000000000000000
χ554444-4-4-4-4400004-4-44-4-440000000000000000000000000000000000000000004i−4i00000000000000000000
χ564444-4-4-4-4400004-4-44-4-44000000000000000000000000000000000000000000−4i4i00000000000000000000
χ5744-4-444-4-44000044-4-44-4-44i−4i000000000000000000000000004i−4i0000000000000000000000000000000000
χ5844-4-444-4-44000044-4-44-4-4−4i4i00000000000000000000000000−4i4i0000000000000000000000000000000000
χ5944-4-444-4-4-20000-2-222-2224i−4i00000000000000000000000000−2i2i00i6−i6i6−i66−66−6000000000000000000000000
χ6044-4-444-4-4-20000-2-222-2224i−4i00000000000000000000000000−2i2i00−i6i6−i6i6−66−66000000000000000000000000
χ6144-4-444-4-4-20000-2-222-222−4i4i000000000000000000000000002i−2i00i6−i6i6−i6−66−66000000000000000000000000
χ6244-4-444-4-4-20000-2-222-222−4i4i000000000000000000000000002i−2i00−i6i6−i6i66−66−6000000000000000000000000
χ6344-4-4-4-444-244-4-4-22-222-220000-2-2220000000000004i−4i00000000000000000000000000−2i2i00000000000000
χ6444-4-4-4-444-244-4-4-22-222-220000-2-222000000000000−4i4i000000000000000000000000002i−2i00000000000000
χ6544-4-4-4-444-2-4-444-22-222-22000022-2-2000000004-400000000000000000000000000-22000000000000000000
χ6644-4-4-4-444-2-4-444-22-222-22000022-2-200000000-44000000000000000000000000002-2000000000000000000
χ674-44-44-44-440000-4-4-4-4444004-4000000000000000000000000004-400000000000000000000000000000000
χ684-44-44-44-440000-4-4-4-444400-4400000000000000000000000000-4400000000000000000000000000000000
χ694-44-44-44-4-200002222-2-2-2004-400000000000000000000000000-22i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ704-44-44-44-4-200002222-2-2-2004-400000000000000000000000000-22−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ714-44-44-44-4-200002222-2-2-200-44000000000000000000000000002-2i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ724-44-44-44-4-200002222-2-2-200-44000000000000000000000000002-2−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ734-44-4-44-44-24-44-42-2-2222-20000-22-22000000000000004i−4i00000000000000000000000000−2i2i000000000000
χ744-44-4-44-44-24-44-42-2-2222-20000-22-2200000000000000−4i4i000000000000000000000000002i−2i000000000000
χ754-44-4-44-44-2-44-442-2-2222-200002-22-200000000004-400000000000000000000000000-220000000000000000
χ764-44-4-44-44-2-44-442-2-2222-200002-22-20000000000-44000000000000000000000000002-20000000000000000
χ774-4-444-4-44-24-4-4422-2-2-2220000-222-200000000000000004-4000000-2-2220000000000000000000000000000
χ784-4-444-4-44-24-4-4422-2-2-2220000-222-20000000000000000-4400000022-2-20000000000000000000000000000
χ794-4-444-4-44-2-444-422-2-2-22200002-2-220000000000000000004i−4i00000000−2i−2i2i2i000000000000000000000000
χ804-4-444-4-44-2-444-422-2-2-22200002-2-22000000000000000000−4i4i000000002i2i−2i−2i000000000000000000000000
χ814-4-44-444-440000-44-44-44-400000000000000000000000000000000000000004-40000000000000000000000
χ824-4-44-444-440000-44-44-44-40000000000000000000000000000000000000000-440000000000000000000000
χ838888-8-8-8-8-40000-444-444-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-888-8-400004-44-44-440000000000000000000000000000000000000000000000000000000000000000

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