Finite Group Databasebeta

← Group #10823493

Character table — Group #10823493

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444466666666888888888888888888888888121212121616161616161616242424242424242424242424
order122222223444466666668888121212124444444444444444448812121212242424242424242488881212121212121212222224444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-1
χ3111111111111111111111111111111111111-1-11-1-11-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111
χ4111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-11111-1-1-1-1-1-1-1
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
χ61111111111111111111111111111-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111111
χ911111111111111111111-1-1-1-1111111111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111-1-111-1-11-1-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-11111-1-1-111
χ1111111111111111111111-1-1-1-1111111111111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-111-1-1111-1-1
χ1211111111111111111111-1-1-1-1111111111111-1-1-111-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-111-1-1-1-111-111
χ1311111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-111-1-111-111
χ1411111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111111-1-1-1-1111-1-1
χ1511111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-111-1-111-1-1-111
χ1611111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-111-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-11-1-11111-1-11-1-1
χ17222222222-2-2-2-222222220000-2-2-2-22222-2-2-2-200200-200000022-2-200000000000000000000-200000000200
χ18222222222-2-2-2-222222220000-2-2-2-22222-2-2-2-200-2002000000-2-22200000000000000000000200000000-200
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2222200200-200000022-2-200000000000000000000200000000-200
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2222200-2002000000-2-22200000000000000000000-200000000200
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
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-10000000022-222-2-2-2-2-2-2-21111-1-1-1-111110000-1-1-1-11111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-100000000-2-22-2-22-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1000011111111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-100000000-2-2-2-2-2-22222-2-21111-1-1-1-1111100001111-1-1-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-100000000222-2-2222-2-2-2-2-1-1-1-1111111110000-1-111-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000000022-2-2-2-2-2-2222211111111-1-1-1-10000-1-11111-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-100000000-2-22222-2-222-2-2-1-1-1-111111111000011-1-111-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-100000000-2-2-222-222-2-22211111111-1-1-1-1000011-1-1-1-111000000000000
χ2922-22-2-22-2222-2-22-2-22-22-20000-2-2222i2i−2i−2i2i2i−2i−2i0000002i−2i0000000000000000000000002i−2i0002-2000000000
χ3022-22-2-22-2222-2-22-2-22-22-20000-2-2222i2i−2i−2i2i2i−2i−2i000000−2i2i000000000000000000000000−2i2i000-22000000000
χ3122-22-2-22-2222-2-22-2-22-22-20000-2-222−2i−2i2i2i−2i−2i2i2i0000002i−2i0000000000000000000000002i−2i000-22000000000
χ3222-22-2-22-2222-2-22-2-22-22-20000-2-222−2i−2i2i2i−2i−2i2i2i000000−2i2i000000000000000000000000−2i2i0002-2000000000
χ3322-22-2-22-22-2-2222-2-22-22-2000022-2-22i2i−2i−2i−2i−2i2i2i2-2000000000000000000000000002-2000000000002i−2i00000
χ3422-22-2-22-22-2-2222-2-22-22-2000022-2-22i2i−2i−2i−2i−2i2i2i-2200000000000000000000000000-2200000000000−2i2i00000
χ3522-22-2-22-22-2-2222-2-22-22-2000022-2-2−2i−2i2i2i2i2i−2i−2i2-2000000000000000000000000002-200000000000−2i2i00000
χ3622-22-2-22-22-2-2222-2-22-22-2000022-2-2−2i−2i2i2i2i2i−2i−2i-2200000000000000000000000000-22000000000002i−2i00000
χ372-22-2-222-222-22-2-2222-2-2-200002-22-22i−2i2i−2i2i−2i2i−2i00000000002-20000000022-2-200000000000000000000002i−2i
χ382-22-2-222-222-22-2-2222-2-2-200002-22-22i−2i2i−2i2i−2i2i−2i0000000000-2200000000-2-2220000000000000000000000−2i2i
χ392-22-2-222-222-22-2-2222-2-2-200002-22-2−2i2i−2i2i−2i2i−2i2i00000000002-20000000022-2-20000000000000000000000−2i2i
χ402-22-2-222-222-22-2-2222-2-2-200002-22-2−2i2i−2i2i−2i2i−2i2i0000000000-2200000000-2-22200000000000000000000002i−2i
χ412-22-2-222-22-22-22-2222-2-2-222-2-2-22-222i−2i2i−2i−2i2i−2i2i000000000000000022-2-200002i2i−2i−2i00000000000000000000
χ422-22-2-222-22-22-22-2222-2-2-222-2-2-22-22−2i2i−2i2i2i−2i2i−2i000000000000000022-2-20000−2i−2i2i2i00000000000000000000
χ432-22-2-222-22-22-22-2222-2-2-2-2-222-22-222i−2i2i−2i−2i2i−2i2i0000000000000000-2-2220000−2i−2i2i2i00000000000000000000
χ442-22-2-222-22-22-22-2222-2-2-2-2-222-22-22−2i2i−2i2i2i−2i2i−2i0000000000000000-2-22200002i2i−2i−2i00000000000000000000
χ452-2-2-22-22222-2-22-2-2-222-220000-222-22-2-222-2-220002-200000000000000000000000002-2000000000002-2000
χ462-2-2-22-22222-2-22-2-2-222-220000-222-22-2-222-2-22000-220000000000000000000000000-2200000000000-22000
χ472-2-2-22-22222-2-22-2-2-222-220000-222-2-222-2-222-20002-200000000000000000000000002-200000000000-22000
χ482-2-2-22-22222-2-22-2-2-222-220000-222-2-222-2-222-2000-220000000000000000000000000-22000000000002-2000
χ492-2-2-22-2222-222-2-2-2-222-2200002-2-222-2-22-222-2000000002-20000000000000000000000002-20002-20000000
χ502-2-2-22-2222-222-2-2-2-222-2200002-2-222-2-22-222-200000000-22000000000000000000000000-22000-220000000
χ512-2-2-22-2222-222-2-2-2-222-2200002-2-22-222-22-2-22000000002-20000000000000000000000002-2000-220000000
χ522-2-2-22-2222-222-2-2-2-222-2200002-2-22-222-22-2-2200000000-22000000000000000000000000-220002-20000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2000022220000000000400-4000000-2-22200000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2000022220000000000-400400000022-2-200000000000000000000000000000000
χ55444-44-4-4-44000044-4-44-4-422−2222−22000000000000000000000000000022−2222−220000000000000000000000000000
χ56444-44-4-4-44000044-4-44-4-4−2222−22220000000000000000000000000000−2222−22220000000000000000000000000000
χ57444-44-4-4-4-20000-2-222-22222−2222−22000000000000000000000000−2i32i300−22−22i6−i6i6−i6000000000000000000000000
χ58444-44-4-4-4-20000-2-222-22222−2222−220000000000000000000000002i3−2i300−22−22−i6i6−i6i6000000000000000000000000
χ59444-44-4-4-4-20000-2-222-222−2222−2222000000000000000000000000−2i32i3002−22−2−i6i6−i6i6000000000000000000000000
χ60444-44-4-4-4-20000-2-222-222−2222−22220000000000000000000000002i3−2i3002−22−2i6−i6i6−i6000000000000000000000000
χ6144-44-4-44-4-244-4-4-222-22-22000022-2-2000000000000004i−4i000000000000000000000000−2i2i00000000000000
χ6244-44-4-44-4-244-4-4-222-22-22000022-2-200000000000000−4i4i0000000000000000000000002i−2i00000000000000
χ6344-44-4-44-4-2-4-444-222-22-220000-2-222000000004-400000000000000000000000000-22000000000000000000
χ6444-44-4-44-4-2-4-444-222-22-220000-2-22200000000-44000000000000000000000000002-2000000000000000000
χ6544-4-4-44-44400004-44-4-4-44000000000000000000000000000000000000000022−2222−2200000000000000000000
χ6644-4-4-44-44400004-44-4-4-440000000000000000000000000000000000000000−2222−222200000000000000000000
χ674-444-4-4-4440000-44-4-4-44422−22−2222000000000000000000000000000022−22−22220000000000000000000000000000
χ684-444-4-4-4440000-44-4-4-444−222222−220000000000000000000000000000−222222−220000000000000000000000000000
χ694-444-4-4-44-200002-2222-2-222−22−222200000000000000000000000000−2i32i3−222−2i6−i6−i6i6000000000000000000000000
χ704-444-4-4-44-200002-2222-2-222−22−2222000000000000000000000000002i3−2i3−222−2−i6i6i6−i6000000000000000000000000
χ714-444-4-4-44-200002-2222-2-2−222222−2200000000000000000000000000−2i32i32−2−22−i6i6i6−i6000000000000000000000000
χ724-444-4-4-44-200002-2222-2-2−222222−22000000000000000000000000002i3−2i32−2−22i6−i6−i6i6000000000000000000000000
χ734-44-4-444-4-24-44-42-2-2-22220000-22-220000000000000000004-400000000-2-222000000000000000000000000
χ744-44-4-444-4-24-44-42-2-2-22220000-22-22000000000000000000-440000000022-2-2000000000000000000000000
χ754-44-4-444-4-2-44-442-2-2-222244-4-42-22-2000000000000000000000000-2-2220000000000000000000000000000
χ764-44-4-444-4-2-44-442-2-2-2222-4-4442-22-200000000000000000000000022-2-20000000000000000000000000000
χ774-4-4444-4-440000-4-44-444-40000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ784-4-4444-4-440000-4-44-444-400000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ794-4-4-44-444-24-4-44222-2-22-200002-2-22000000000004-40000000000000000000000000-220000000000000000
χ804-4-4-44-444-24-4-44222-2-22-200002-2-2200000000000-4400000000000000000000000002-20000000000000000
χ814-4-4-44-444-2-444-4222-2-22-20000-222-200000000000000004-4000000000000000000000000-22000000000000
χ824-4-4-44-444-2-444-4222-2-22-20000-222-20000000000000000-440000000000000000000000002-2000000000000
χ8388-8-8-88-88-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-8888-8-8-4000044-44-4-440000000000000000000000000000000000000000000000000000000000000000

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