Finite Group Databasebeta

← Group #10877316

Character table — Group #10877316

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212161616162424242424242424242424242424
order12222222344446666666444412121212121212122244444466668888121212121212242424242424242422441212121244444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111111111111111-1-1-1-1111-1-1-1-1111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1111-1-1-1-1111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111
χ1111111111111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-111-1-1
χ1311111111111111111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1111-1-1-1-11-1-111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-1111-1-1-1-11-1-111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ17222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-200000000000000002200000000000022-2-20000-22000000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2000000000000000022000000000000-2-22200002-2000000000000
χ19222222222-2-2-2-22222222-2-222-2-2-22222-20000000000000000-2-200000000000022-2-200002-2000000000000
χ20222222222-2-2-2-22222222-2-222-2-2-22222-20000000000000000-2-2000000000000-2-2220000-22000000000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111110000111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-222221111-2-2-2-2-1-11111111111110000-1-1-1-100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-10000111100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-11111-122-2-222-2-2-1-1-1-122-2-2111111-1-1-1-111110000-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-11111-122-2-2-2-222-1-1-1-1-2-2221111111111-1-1-1-1000011-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-11111-1-2-22222-2-21111-2-22211-1-1-1-11111-1-1-1-10000-1-11100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-11111-1-2-222-2-222111122-2-211-1-1-1-1-1-1-1-11111000011-1-100000000000000
χ29222-22-2-2-2222-2-2222-2-2-2-2000022-20000-22-200000022-2-20000000000000000002-22-20000002-20000000000
χ30222-22-2-2-2222-2-2222-2-2-2-2000022-20000-22-200000022-2-2000000000000000000-22-22000000-220000000000
χ31222-22-2-2-2222-2-2222-2-2-2-2000022-20000-2-22000000-2-2220000000000000000002-22-2000000-220000000000
χ32222-22-2-2-2222-2-2222-2-2-2-2000022-20000-2-22000000-2-222000000000000000000-22-220000002-20000000000
χ33222-22-2-2-22-2-222222-2-2-2-20000-2-2200002002i−2i000000000000002i2i−2i−2i000000002-2-22000000002i−2i00000000
χ34222-22-2-2-22-2-222222-2-2-2-20000-2-2200002002i−2i000000000000002i2i−2i−2i00000000-222-200000000−2i2i00000000
χ35222-22-2-2-22-2-222222-2-2-2-20000-2-220000200−2i2i00000000000000−2i−2i2i2i000000002-2-2200000000−2i2i00000000
χ36222-22-2-2-22-2-222222-2-2-2-20000-2-220000200−2i2i00000000000000−2i−2i2i2i00000000-222-2000000002i−2i00000000
χ372-222-22-2-222-22-2-2-222-2-222-22-22-2-222-2-2200000000000000002-2000000000000000000000000002i−2i2i−2i0000
χ382-222-22-2-222-22-2-2-222-2-222-22-22-2-222-2-2200000000000000002-200000000000000000000000000−2i2i−2i2i0000
χ392-222-22-2-222-22-2-2-222-2-22-22-222-2-2-2-22220000000000000000-22000000000000000000000000002i−2i−2i2i0000
χ402-222-22-2-222-22-2-2-222-2-22-22-222-2-2-2-22220000000000000000-2200000000000000000000000000−2i2i2i−2i0000
χ412-222-22-2-22-22-22-2-222-2-222-2-22-222-2-222-200002i−2i2i−2i000000002-200000000000000002i−2i2i−2i00000000000000
χ422-222-22-2-22-22-22-2-222-2-222-2-22-222-2-222-20000−2i2i−2i2i000000002-20000000000000000−2i2i−2i2i00000000000000
χ432-222-22-2-22-22-22-2-222-2-22-222-2-22222-2-2-200002i−2i−2i2i00000000-2200000000000000002i−2i−2i2i00000000000000
χ442-222-22-2-22-22-22-2-222-2-22-222-2-22222-2-2-20000−2i2i2i−2i00000000-220000000000000000−2i2i2i−2i00000000000000
χ452-222-22-2-2-1-22-2211-1-111-12-2-221-1-111-1-1100002i−2i2i−2i−i3i3−i3i30000-11−i3i3−i3i333−3−333−3−30000−ii−ii00000000000000
χ462-222-22-2-2-1-22-2211-1-111-12-2-221-1-111-1-1100002i−2i2i−2ii3−i3i3−i30000-11i3−i3i3−i3−3−333−3−3330000−ii−ii00000000000000
χ472-222-22-2-2-1-22-2211-1-111-12-2-221-1-111-1-110000−2i2i−2i2i−i3i3−i3i30000-11−i3i3−i3i3−3−333−3−3330000i−ii−i00000000000000
χ482-222-22-2-2-1-22-2211-1-111-12-2-221-1-111-1-110000−2i2i−2i2ii3−i3i3−i30000-11i3−i3i3−i333−3−333−3−30000i−ii−i00000000000000
χ492-222-22-2-2-1-22-2211-1-111-1-222-21-1-1-1-111100002i−2i−2i2i−i3i3−i3i300001-1i3−i3i3−i333−3−3−3−3330000−iii−i00000000000000
χ502-222-22-2-2-1-22-2211-1-111-1-222-21-1-1-1-111100002i−2i−2i2ii3−i3i3−i300001-1−i3i3−i3i3−3−33333−3−30000−iii−i00000000000000
χ512-222-22-2-2-1-22-2211-1-111-1-222-21-1-1-1-11110000−2i2i2i−2i−i3i3−i3i300001-1i3−i3i3−i3−3−33333−3−30000i−i−ii00000000000000
χ522-222-22-2-2-1-22-2211-1-111-1-222-21-1-1-1-11110000−2i2i2i−2ii3−i3i3−i300001-1−i3i3−i3i333−3−3−3−3330000i−i−ii00000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4222222220000000000000000-2-20000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444222-2-2-2-220000000000000000220000000000000000000000000000000000
χ55444-44-4-4-4-244-4-4-2-2-222220000-2-22000024-4000000-2-2220000000000000000000000000000000000000000
χ56444-44-4-4-4-244-4-4-2-2-222220000-2-2200002-4400000022-2-20000000000000000000000000000000000000000
χ57444-44-4-4-4-2-4-444-2-2-22222000022-20000-2004i−4i00000000000000−2i−2i2i2i000000000000000000000000000000
χ58444-44-4-4-4-2-4-444-2-2-22222000022-20000-200−4i4i000000000000002i2i−2i−2i000000000000000000000000000000
χ5944-44-4-4-44400004-4-444-4-4000000000000000000000000−2i22i200000000−2i22i2−2i22i200000000000000000000000000
χ6044-44-4-4-44400004-4-444-4-40000000000000000000000002i2−2i2000000002i2−2i22i2−2i200000000000000000000000000
χ6144-44-4-4-44-20000-222-2-222000000023−2323−230000000000000−2i22i200000000i2−i2i2−i2i6−i6i6−i60000000000000000000000
χ6244-44-4-4-44-20000-222-2-222000000023−2323−2300000000000002i2−2i200000000−i2i2−i2i2−i6i6−i6i60000000000000000000000
χ6344-44-4-4-44-20000-222-2-2220000000−2323−23230000000000000−2i22i200000000i2−i2i2−i2−i6i6−i6i60000000000000000000000
χ6444-44-4-4-44-20000-222-2-2220000000−2323−232300000000000002i2−2i200000000−i2i2−i2i2i6−i6i6−i60000000000000000000000
χ6544-4-4-444-4400004-4-4-4-444000000000000000000000000000000000000000000000000000000000000−2i22i200
χ6644-4-4-444-4400004-4-4-4-4440000000000000000000000000000000000000000000000000000000000002i2−2i200
χ674-444-44-4-4-24-44-422-2-222-24-44-4-222-2-222-20000000000000000-220000000000000000000000000000000000
χ684-444-44-4-4-24-44-422-2-222-2-44-44-22222-2-2-200000000000000002-20000000000000000000000000000000000
χ694-44-4-4-44444-4-44-4-44-444-400004-440000-40000000000000000000000000000000000000000000000000000
χ704-44-4-4-4444-444-4-4-44-444-40000-44-4000040000000000000000000000000000000000000000000000000000
χ714-44-4-4-444-24-4-4422-22-2-220000-22-20000200000000000000000023−23−2323000000000000000000000000000000
χ724-44-4-4-444-24-4-4422-22-2-220000-22-200002000000000000000000−232323−23000000000000000000000000000000
χ734-44-4-4-444-2-444-422-22-2-2200002-220000-200000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ744-44-4-4-444-2-444-422-22-2-2200002-220000-2000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ754-4-444-44-440000-44-44-44-400000000000000000000000000−2i22i20000000000−2i22i22i2−2i20000000000000000000000
χ764-4-444-44-440000-44-44-44-4000000000000000000000000002i2−2i200000000002i2−2i2−2i22i20000000000000000000000
χ774-4-444-44-4-200002-22-22-22000000023−23−2323000000000000000−2i22i2000000i6−i6−i6i6i2−i2−i2i20000000000000000000000
χ784-4-444-44-4-200002-22-22-22000000023−23−23230000000000000002i2−2i2000000−i6i6i6−i6−i2i2i2−i20000000000000000000000
χ794-4-444-44-4-200002-22-22-220000000−232323−23000000000000000−2i22i2000000−i6i6i6−i6i2−i2−i2i20000000000000000000000
χ804-4-444-44-4-200002-22-22-220000000−232323−230000000000000002i2−2i2000000i6−i6−i6i6−i2i2i2−i20000000000000000000000
χ814-4-4-444-4440000-44-4-44-440000000000000000000000000000000000000000000000000000000000000022−22
χ824-4-4-444-4440000-44-4-44-4400000000000000000000000000000000000000000000000000000000000000−2222
χ8388-8-8-888-8-40000-44444-4-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-888-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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