Finite Group Databasebeta

← Group #10844801

Character table — Group #10844801

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444444446666666441212121212121212444488881212121212121212121224242424242424248888888844121212122244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ911111111111-1-1-1-1111111111-1-1111-1-1-1-1111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-1-1-11-1111-11-1
χ1011111111111-1-1-1-1111111111-1-1111-1-1-1-1111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-111-1-111-11-1-1-11-11
χ1111111111111-1-1-1-1111111111-1-1111-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111-1-1-1111-11-11
χ1211111111111-1-1-1-1111111111-1-1111-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-111111-1-1-11-11-1
χ1311111111111-1-1-1-1111111111-1-1111-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-1-111111-1-1-11-1-11
χ1411111111111-1-1-1-1111111111-1-1111-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-1-111-1-1-1111-111-1
χ1511111111111-1-1-1-1111111111-1-1111-1-1-1-11-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-111-1-111-11-1-1-111-1
χ1611111111111-1-1-1-1111111111-1-1111-1-1-1-11-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-111-1-1-1-11-1111-1-11
χ17222222222-2-22222-2-22222222-2-2-2-2-22222-200000000-2-2000000000000000000000000000000002200-2-200
χ18222222222-2-22222-2-22222222-2-2-2-2-22222-200000000-2-200000000000000000000000000000000-2-2002200
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000022000000000000000000000000000000002-200-2200
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000002200000000000000000000000000000000-22002-200
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-10000000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-222-2-211-1-1-1-11111-1-1-1-11111000000002-2-1-1110000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2-2-22211-1-1-1-111111111-1-1-1-100000000-2211-1-10000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-22222-2-2111111-1-1-1-1-1-1-1-1111100000000-2211-1-10000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-222-2-222111111-1-1-1-11111-1-1-1-1000000002-2-1-1110000000000
χ2922-22-2-22-222-20000-222-22-2-22-2002-2-200002002i−2i00000000002i2i−2i−2i000000002i2i−2i−2i00000000002-200000000
χ3022-22-2-22-222-20000-222-22-2-22-2002-2-200002002i−2i00000000002i2i−2i−2i00000000−2i−2i2i2i0000000000-2200000000
χ3122-22-2-22-222-20000-222-22-2-22-2002-2-20000200−2i2i0000000000−2i−2i2i2i000000002i2i−2i−2i0000000000-2200000000
χ3222-22-2-22-222-20000-222-22-2-22-2002-2-20000200−2i2i0000000000−2i−2i2i2i00000000−2i−2i2i2i00000000002-200000000
χ332-22-22-22-222-200002-2-222-2-2-220022-20000-22i−2i000000002i2i−2i−2i0000000000002-22-2000000000000002i−2i0000
χ342-22-22-22-222-200002-2-222-2-2-220022-20000-22i−2i000000002i2i−2i−2i000000000000-22-2200000000000000−2i2i0000
χ352-22-22-22-222-200002-2-222-2-2-220022-20000-2−2i2i00000000−2i−2i2i2i0000000000002-22-200000000000000−2i2i0000
χ362-22-22-22-222-200002-2-222-2-2-220022-20000-2−2i2i00000000−2i−2i2i2i000000000000-22-22000000000000002i−2i0000
χ372-2-2-2-222222222-2-2-2-2-2-2222-2-22-22-2222-2-2-2000000002-200000000000000002i−2i−2i2i2i2i−2i−2i0000000000000000
χ382-2-2-2-222222222-2-2-2-2-2-2222-2-22-22-2222-2-2-2000000002-20000000000000000−2i2i2i−2i−2i−2i2i2i0000000000000000
χ392-2-2-2-2222222-2-222-2-2-2-2222-2-2-222-22-2-222-200000000-2200000000000000002i−2i−2i2i−2i−2i2i2i0000000000000000
χ402-2-2-2-2222222-2-222-2-2-2-2222-2-2-222-22-2-222-200000000-220000000000000000−2i2i2i−2i2i2i−2i−2i0000000000000000
χ412-2-2-2-22222-2-222-2-222-2-2222-2-2-22-22-222-2-2200002-22-2-220000000022-2-222-2-2000000000000000000000000
χ422-2-2-2-22222-2-222-2-222-2-2222-2-2-22-22-222-2-220000-22-22-2200000000-2-222-2-222000000000000000000000000
χ432-2-2-2-22222-2-2-2-22222-2-2222-2-22-2-22-2-2-222200002-2-222-20000000022-2-2-2-222000000000000000000000000
χ442-2-2-2-22222-2-2-2-22222-2-2222-2-22-2-22-2-2-22220000-222-22-200000000-2-22222-2-2000000000000000000000000
χ452-2-2-2-2222-1-2-222-2-22211-1-1-111-221-11-1-111-100002-22-21-13−33−33−33−3-1-111-1-11100000000003−33−30000000000
χ462-2-2-2-2222-1-2-222-2-22211-1-1-111-221-11-1-111-100002-22-21-1−33−33−33−33-1-111-1-1110000000000−33−330000000000
χ472-2-2-2-2222-1-2-222-2-22211-1-1-111-221-11-1-111-10000-22-221-13−33−33−33−311-1-111-1-10000000000−33−330000000000
χ482-2-2-2-2222-1-2-222-2-22211-1-1-111-221-11-1-111-10000-22-221-1−33−33−33−3311-1-111-1-100000000003−33−30000000000
χ492-2-2-2-2222-1-2-2-2-2222211-1-1-1112-21-1111-1-1-100002-2-22-113−33−3−33−33-1-11111-1-100000000003−3−330000000000
χ502-2-2-2-2222-1-2-2-2-2222211-1-1-1112-21-1111-1-1-100002-2-22-11−33−333−33−3-1-11111-1-10000000000−333−30000000000
χ512-2-2-2-2222-1-2-2-2-2222211-1-1-1112-21-1111-1-1-10000-222-2-113−33−3−33−3311-1-1-1-1110000000000−333−30000000000
χ522-2-2-2-2222-1-2-2-2-2222211-1-1-1112-21-1111-1-1-10000-222-2-11−33−333−33−311-1-1-1-11100000000003−3−330000000000
χ5344444444-2-4-44444-4-4-2-2-2-2-2-2-2-4-4222-2-2-2-2200000000220000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2442222222200000000-2-20000000000000000000000000000000000000000
χ55444-4-4-4-444004-44-40044-44-4-4-4000004-44-4000000000000000000000000000000000000000000000000000
χ56444-4-4-4-44400-44-440044-44-4-4-400000-44-44000000000000000000000000000000000000000000000000000
χ57444-4-4-4-44-2004-44-400-2-22-222200000-22-220000000000000000000i6−i6i6−i6i6−i6i6−i6000000000000000000000000
χ58444-4-4-4-44-2004-44-400-2-22-222200000-22-220000000000000000000−i6i6−i6i6−i6i6−i6i6000000000000000000000000
χ59444-4-4-4-44-200-44-4400-2-22-2222000002-22-20000000000000000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ60444-4-4-4-44-200-44-4400-2-22-2222000002-22-20000000000000000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ6144-44-4-44-44-4400004-44-44-4-44-400-4440000-400000000000000000000000000000000000000000000000000
χ6244-44-4-44-4-24-40000-44-22-222-2200-2220000-2004i−4i0000000000−2i−2i2i2i00000000000000000000000000000000
χ6344-44-4-44-4-24-40000-44-22-222-2200-2220000-200−4i4i00000000002i2i−2i−2i00000000000000000000000000000000
χ6444-44-4-44-4-2-4400004-4-22-222-22002-2-2000020000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ6544-44-4-44-4-2-4400004-4-22-222-22002-2-20000200000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ6644-4-444-4-44000000004-4-4-44-440000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ6744-4-444-4-44000000004-4-4-44-4400000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ684-444-44-4-4400000000-44-4-444-4000000000000000000000000000000000000000022−22−22220000000000000000
χ694-444-44-4-4400000000-44-4-444-40000000000000000000000000000000000000000−222222−220000000000000000
χ704-44-44-44-44-440000-44-444-4-4-4400-4-440000400000000000000000000000000000000000000000000000000
χ714-44-44-44-4-24-400004-42-2-2222-200-2-22000024i−4i00000000−2i−2i2i2i000000000000000000000000000000000000
χ724-44-44-44-4-24-400004-42-2-2222-200-2-2200002−4i4i000000002i2i−2i−2i000000000000000000000000000000000000
χ734-44-44-44-4-2-440000-442-2-2222-20022-20000-200000000000000−2i32i32i3−2i300000000000000000000000000000000
χ744-44-44-44-4-2-440000-442-2-2222-20022-20000-2000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ754-4-444-4-444004-4-4400-4-4-44-444000004-4-44000000000000000000000000000000000000000000000000000
χ764-4-444-4-44400-444-400-4-4-44-44400000-444-4000000000000000000000000000000000000000000000000000
χ774-4-444-4-44-2004-4-4400222-22-2-200000-222-20000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ784-4-444-4-44-2004-4-4400222-22-2-200000-222-20000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ794-4-444-4-44-200-444-400222-22-2-2000002-2-220000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ804-4-444-4-44-200-444-400222-22-2-2000002-2-220000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ814-4-4-4-4444-24444-4-4-4-422-2-2-2224-4-22-2-2-222200000000-220000000000000000000000000000000000000000
χ824-4-4-4-4444-244-4-444-4-422-2-2-222-44-22-222-2-22000000002-20000000000000000000000000000000000000000
χ8388-8-888-8-8-400000000-4444-44-4000000000000000000000000000000000000000000000000000000000000
χ848-888-88-8-8-4000000004-444-4-44000000000000000000000000000000000000000000000000000000000000

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