Finite Group Databasebeta

← Group #10896431

Character table — Group #10896431

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212161616162424242424242424242424242424
order1222222234444666666644441212121212121212224444448888121212121212121212122424242424242424444466121244444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ17222222222-2-2-2-2222222222-2-22222-2-2-2-2000000000000-2-2000000000000000022-2-20000-22000000000000
χ18222222222-2-2-2-2222222222-2-22222-2-2-2-2000000000000-2-20000000000000000-2-22200002-2000000000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-200000000000022000000000000000022-2-200002-2000000000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2000000000000220000000000000000-2-2220000-22000000000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-111111111111111110000-1-1-1-100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000111100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-10000111100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-122-2-222-2-222-2-211-1-1-1-11111-1-1-1-111110000-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-122-2-2-2-222-2-222111111-1-1-1-11111-1-1-1-10000-1-11100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-1-2-22222-2-2-2-22211-1-1-1-111111111-1-1-1-1000011-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-1-2-222-2-22222-2-2111111-1-1-1-1-1-1-1-11111000011-1-100000000000000
χ292222-2-2-2-2222-2-2-2-222-2-222-22-222-2-222-2-22-22-2000000002-2000000000000000000002-22-200000000000000
χ302222-2-2-2-2222-2-2-2-222-2-222-22-222-2-222-2-2-22-22000000002-200000000000000000000-22-2200000000000000
χ312222-2-2-2-2222-2-2-2-222-2-22-22-22-2-22222-2-22-2-2200000000-22000000000000000000002-2-2200000000000000
χ322222-2-2-2-2222-2-2-2-222-2-22-22-22-2-22222-2-2-222-200000000-2200000000000000000000-222-200000000000000
χ332222-2-2-2-22-2-222-2-222-2-222-2-2222-2-2-2-222000000000000-220000000000000000000000000000002i−2i2i−2i0000
χ342222-2-2-2-22-2-222-2-222-2-222-2-2222-2-2-2-222000000000000-22000000000000000000000000000000−2i2i−2i2i0000
χ352222-2-2-2-22-2-222-2-222-2-22-222-2-2-222-2-2220000000000002-20000000000000000000000000000002i−2i−2i2i0000
χ362222-2-2-2-22-2-222-2-222-2-22-222-2-2-222-2-2220000000000002-2000000000000000000000000000000−2i2i2i−2i0000
χ372222-2-2-2-2-122-2-211-1-111-12-22-2-1-111-1-1112-22-200000000-1133−3−333−3−333−3−333−3−30000-11-1100000000000000
χ382222-2-2-2-2-122-2-211-1-111-12-22-2-1-111-1-1112-22-200000000-11−3−333−3−333−3−333−3−3330000-11-1100000000000000
χ392222-2-2-2-2-122-2-211-1-111-12-22-2-1-111-1-111-22-2200000000-1133−3−333−3−3−3−333−3−33300001-11-100000000000000
χ402222-2-2-2-2-122-2-211-1-111-12-22-2-1-111-1-111-22-2200000000-11−3−333−3−33333−3−333−3−300001-11-100000000000000
χ412222-2-2-2-2-122-2-211-1-111-1-22-2211-1-1-1-1112-2-22000000001-133−3−3−3−33333−3−3−3−3330000-111-100000000000000
χ422222-2-2-2-2-122-2-211-1-111-1-22-2211-1-1-1-1112-2-22000000001-1−3−33333−3−3−3−33333−3−30000-111-100000000000000
χ432222-2-2-2-2-122-2-211-1-111-1-22-2211-1-1-1-111-222-2000000001-133−3−3−3−333−3−33333−3−300001-1-1100000000000000
χ442222-2-2-2-2-122-2-211-1-111-1-22-2211-1-1-1-111-222-2000000001-1−3−33333−3−333−3−3−3−33300001-1-1100000000000000
χ452-2-2222-2-222-22-22-2-2-22-22000000002-2-2200002-2000000002-22-20000000000002i−2i2i−2i000000002i−2i00000000
χ462-2-2222-2-222-22-22-2-2-22-22000000002-2-2200002-2000000002-22-2000000000000−2i2i−2i2i00000000−2i2i00000000
χ472-2-2222-2-222-22-22-2-2-22-22000000002-2-220000-2200000000-22-220000000000002i−2i2i−2i00000000−2i2i00000000
χ482-2-2222-2-222-22-22-2-2-22-22000000002-2-220000-2200000000-22-22000000000000−2i2i−2i2i000000002i−2i00000000
χ492-2-2222-2-22-22-222-2-2-22-2200000000-222-20000002i−2i00000000002i−2i2i−2i000000002i−2i−2i2i0000002-20000000000
χ502-2-2222-2-22-22-222-2-2-22-2200000000-222-20000002i−2i00000000002i−2i2i−2i00000000−2i2i2i−2i000000-220000000000
χ512-2-2222-2-22-22-222-2-2-22-2200000000-222-2000000−2i2i0000000000−2i2i−2i2i000000002i−2i−2i2i000000-220000000000
χ522-2-2222-2-22-22-222-2-2-22-2200000000-222-2000000−2i2i0000000000−2i2i−2i2i00000000−2i2i2i−2i0000002-20000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4-2-2-2-222220000000000002200000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44422222222000000000000-2-200000000000000000000000000000000000000
χ554444-4-4-4-4-2-4-44422-2-222-24-4-44-2-22222-2-20000000000002-200000000000000000000000000000000000000
χ564444-4-4-4-4-2-4-44422-2-222-2-444-422-2-222-2-2000000000000-2200000000000000000000000000000000000000
χ5744-4-44-44-440000-4-44-444-400000000000000000000000000000000000000000000000000000000000000−2i22i2
χ5844-4-44-44-440000-4-44-444-4000000000000000000000000000000000000000000000000000000000000002i2−2i2
χ5944-4-4-44-4440000444-4-4-4-4000000000000000000000000000000000000000000000000000000000000−2i22i200
χ6044-4-4-44-4440000444-4-4-4-40000000000000000000000000000000000000000000000000000000000002i2−2i200
χ614-44-44-4-4440000-44-444-4-40000000000000000000000−2i22i200000000000000−2i22i2−2i22i20000000000000000000000
χ624-44-44-4-4440000-44-444-4-400000000000000000000002i2−2i2000000000000002i2−2i22i2−2i20000000000000000000000
χ634-44-44-4-44-200002-22-2-222000023−2323−2300000000000000−2i22i20000000000i6−i6i6−i6i2−i2i2−i20000000000000000000000
χ644-44-44-4-44-200002-22-2-222000023−2323−23000000000000002i2−2i20000000000−i6i6−i6i6−i2i2−i2i20000000000000000000000
χ654-44-44-4-44-200002-22-2-2220000−2323−232300000000000000−2i22i20000000000−i6i6−i6i6i2−i2i2−i20000000000000000000000
χ664-44-44-4-44-200002-22-2-2220000−2323−2323000000000000002i2−2i20000000000i6−i6i6−i6−i2i2−i2i20000000000000000000000
χ674-44-4-444-4400004-4-44-44-400000000000000000000−2i22i2000000000000−2i22i22i2−2i200000000000000000000000000
χ684-44-4-444-4400004-4-44-44-4000000000000000000002i2−2i20000000000002i2−2i2−2i22i200000000000000000000000000
χ694-44-4-444-4-20000-222-22-22000023−23−2323000000000000−2i22i2000000000000i2−i2−i2i2−i6i6i6−i60000000000000000000000
χ704-44-4-444-4-20000-222-22-22000023−23−23230000000000002i2−2i2000000000000−i2i2i2−i2i6−i6−i6i60000000000000000000000
χ714-44-4-444-4-20000-222-22-220000−232323−23000000000000−2i22i2000000000000i2−i2−i2i2i6−i6−i6i60000000000000000000000
χ724-44-4-444-4-20000-222-22-220000−232323−230000000000002i2−2i2000000000000−i2i2i2−i2−i6i6i6−i60000000000000000000000
χ734-4-4444-4-4-24-44-4-2222-22-200000000-222-200004-400000000-22-220000000000000000000000000000000000
χ744-4-4444-4-4-24-44-4-2222-22-200000000-222-20000-44000000002-22-20000000000000000000000000000000000
χ754-4-4444-4-4-2-44-44-2222-22-2000000002-2-220000004i−4i0000000000−2i2i−2i2i000000000000000000000000000000
χ764-4-4444-4-4-2-44-44-2222-22-2000000002-2-22000000−4i4i00000000002i−2i2i−2i000000000000000000000000000000
χ774-4-44-4-44444-4-44-44-4-4-444000000004-44-40000000000000000000000000000000000000000000000000000
χ784-4-44-4-4444-444-4-44-4-4-44400000000-44-440000000000000000000000000000000000000000000000000000
χ794-4-44-4-444-24-4-442-2222-2-200000000-22-220000000000000023−23−23230000000000000000000000000000000000
χ804-4-44-4-444-24-4-442-2222-2-200000000-22-2200000000000000−232323−230000000000000000000000000000000000
χ814-4-44-4-444-2-444-42-2222-2-2000000002-22-2000000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ824-4-44-4-444-2-444-42-2222-2-2000000002-22-20000000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ8388-8-88-88-8-4000044-44-4-440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-88-88-40000-4-4-444440000000000000000000000000000000000000000000000000000000000000000

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