Finite Group Databasebeta

← Group #10830084

Character table — Group #10830084

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order12222222344446666666444444441212121212121212226666888812121212121224242424242424244444441212121222444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-11-111-1-1111-111-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-111-1-1-1-1-11-1-11111-1-111
χ7111111111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-11-1-111-1-11-111-1-111-1-111
χ8111111111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-11-1-11111-11-1-111-1-111-1-1
χ911111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ1011111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ1111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1
χ1211111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111
χ1311111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-11-1-111-1-11-1-1-1111111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-11-1-11111-1111-1-1-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-11-111-1-1111-1-1-111-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111-111-1-1-1-1-1111-1-11111-1-1
χ17222222222-2-2-2-22222222000022-2-2-2-2-22222-20000000000-2-2000000000000222200000000-2-20000000000
χ18222222222-2-2-2-22222222000022-2-2-2-2-22222-20000000000-2-2000000000000-2-2-2-200000000220000000000
χ19222222222-2-2-2-222222220000-2-222-2-2-2-2-2-2-2-200000000002200000000000022-2-200000000-220000000000
χ20222222222-2-2-2-222222220000-2-222-2-2-2-2-2-2-2-2000000000022000000000000-2-222000000002-20000000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111110000-2-2111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-11111-1-2-2111122-2-211-1-1-1-1-1-1-1-1111100002-2-1-11100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-11111-1-2-21111-2-22211-1-1-1-11111-1-1-1-10000-2211-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-2-211112222-1-11111-1-1-1-1-1-1-1-10000-2-2111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-2-21111-2-2-2-2-1-1111111111111000022-1-1-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-11111-122-1-1-1-122-2-2111111-1-1-1-111110000-2211-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-11111-122-1-1-1-1-2-2221111111111-1-1-1-100002-2-1-11100000000000000
χ29222-2-2-22-22-222-2222-2-2-2-22i2i−2i−2i00002-2-2000020000000000002i2i−2i−2i0000000000000000002-2000000002i−2i00
χ30222-2-2-22-22-222-2222-2-2-2-22i2i−2i−2i00002-2-2000020000000000002i2i−2i−2i000000000000000000-2200000000−2i2i00
χ31222-2-2-22-22-222-2222-2-2-2-2−2i−2i2i2i00002-2-200002000000000000−2i−2i2i2i0000000000000000002-200000000−2i2i00
χ32222-2-2-22-22-222-2222-2-2-2-2−2i−2i2i2i00002-2-200002000000000000−2i−2i2i2i000000000000000000-22000000002i−2i00
χ332-2-222-22-222-22-2-2-22-222-22i−2i2i−2i000022-20000-20000000000002i−2i2i−2i000000000000000000000000002i−2i002-2
χ342-2-222-22-222-22-2-2-22-222-22i−2i2i−2i000022-20000-20000000000002i−2i2i−2i00000000000000000000000000−2i2i00-22
χ352-2-222-22-222-22-2-2-22-222-2−2i2i−2i2i000022-20000-2000000000000−2i2i−2i2i000000000000000000000000002i−2i00-22
χ362-2-222-22-222-22-2-2-22-222-2−2i2i−2i2i000022-20000-2000000000000−2i2i−2i2i00000000000000000000000000−2i2i002-2
χ372-2-2-2-2222222-2-2-2-222-2-2200002-22-2-22-222-2-2200000000002-2000000000000000000000000002-22-2000000
χ382-2-2-2-2222222-2-2-2-222-2-2200002-22-2-22-222-2-2200000000002-200000000000000000000000000-22-22000000
χ392-2-2-2-2222222-2-2-2-222-2-220000-22-22-22-2-2-22220000000000-22000000000000000000000000002-2-22000000
χ402-2-2-2-2222222-2-2-2-222-2-220000-22-22-22-2-2-22220000000000-2200000000000000000000000000-222-2000000
χ412-2-2-2-22222-2-222-2-222-2-222-2-222-2-222-2222-2-2-22-222-2-20000-222-2-2200000000000000000000000000000000
χ422-2-2-2-22222-2-222-2-222-2-222-2-22-222-22-22-2-222-2-22-2-22200002-22-2-2200000000000000000000000000000000
χ432-2-2-2-22222-2-222-2-222-2-22-222-22-2-222-2222-2-2-2-22-2-2220000-22-222-200000000000000000000000000000000
χ442-2-2-2-22222-2-222-2-222-2-22-222-2-222-22-22-2-222-22-222-2-200002-2-222-200000000000000000000000000000000
χ452-2-2-2-2222-1-2-22211-1-111-12-2-222-2-22-11-1-1-11112-2-1-11100001-1-111-133−3−333−3−30000003−33−300000000000000
χ462-2-2-2-2222-1-2-22211-1-111-12-2-222-2-22-11-1-1-11112-2-1-11100001-1-111-1−3−333−3−333000000−33−3300000000000000
χ472-2-2-2-2222-1-2-22211-1-111-12-2-22-222-2-11-111-1-11-2211-1-10000-11-111-133−3−3−3−3330000003−3−3300000000000000
χ482-2-2-2-2222-1-2-22211-1-111-12-2-22-222-2-11-111-1-11-2211-1-10000-11-111-1−3−33333−3−3000000−333−300000000000000
χ492-2-2-2-2222-1-2-22211-1-111-1-222-22-2-22-11-1-1-1111-2211-1-100001-11-1-1133−3−333−3−3000000−33−3300000000000000
χ502-2-2-2-2222-1-2-22211-1-111-1-222-22-2-22-11-1-1-1111-2211-1-100001-11-1-11−3−333−3−3330000003−33−300000000000000
χ512-2-2-2-2222-1-2-22211-1-111-1-222-2-222-2-11-111-1-112-2-1-1110000-111-1-1133−3−3−3−333000000−333−300000000000000
χ522-2-2-2-2222-1-2-22211-1-111-1-222-2-222-2-11-111-1-112-2-1-1110000-111-1-11−3−33333−3−30000003−3−3300000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2000044-4-4222-2-2-2-22000000000022000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-444222222220000000000-2-2000000000000000000000000000000000000
χ55444-4-4-44-444-4-44444-4-4-4-400000000-4440000-4000000000000000000000000000000000000000000000000
χ56444-4-4-44-4-24-4-44-2-2-22222000000002-2-20000200−2i32i3−2i32i3000000000000000000000000000000000000000000
χ57444-4-4-44-4-24-4-44-2-2-22222000000002-2-200002002i3−2i32i3−2i3000000000000000000000000000000000000000000
χ58444-4-4-44-4-2-444-4-2-2-222224i4i−4i−4i0000-2220000-2000000000000−2i−2i2i2i00000000000000000000000000000000
χ59444-4-4-44-4-2-444-4-2-2-22222−4i−4i4i4i0000-2220000-20000000000002i2i−2i−2i00000000000000000000000000000000
χ6044-44-44-4-4400004-4-4-44-440000000000000000000000000000000000000000004i−4i00000000000000000000
χ6144-44-44-4-4400004-4-4-44-44000000000000000000000000000000000000000000−4i4i00000000000000000000
χ6244-4-44-4-44400004-4-44-44-4000000000000000000000000−2i22i20000000000−2i22i2−2i22i2000000000000000000000000
χ6344-4-44-4-44400004-4-44-44-40000000000000000000000002i2−2i200000000002i2−2i22i2−2i2000000000000000000000000
χ6444-4-44-4-44-20000-222-22-220000000000023−2323−23000000000−2i22i2000000i6−i6i6−i6i2−i2i2−i2000000000000000000000000
χ6544-4-44-4-44-20000-222-22-220000000000023−2323−230000000002i2−2i2000000−i6i6−i6i6−i2i2−i2i2000000000000000000000000
χ6644-4-44-4-44-20000-222-22-2200000000000−2323−2323000000000−2i22i2000000−i6i6−i6i6i2−i2i2−i2000000000000000000000000
χ6744-4-44-4-44-20000-222-22-2200000000000−2323−23230000000002i2−2i2000000i6−i6i6−i6−i2i2−i2i2000000000000000000000000
χ684-444-4-4-4440000-44-444-4-40000000000000000000000−2i22i200000000−2i22i22i2−2i20000000000000000000000000000
χ694-444-4-4-4440000-44-444-4-400000000000000000000002i2−2i2000000002i2−2i2−2i22i20000000000000000000000000000
χ704-444-4-4-44-200002-22-2-2220000000000023−23−23230000000−2i22i200000000i2−i2−i2i2−i6i6i6−i6000000000000000000000000
χ714-444-4-4-44-200002-22-2-2220000000000023−23−232300000002i2−2i200000000−i2i2i2−i2i6−i6−i6i6000000000000000000000000
χ724-444-4-4-44-200002-22-2-22200000000000−232323−230000000−2i22i200000000i2−i2−i2i2i6−i6−i6i6000000000000000000000000
χ734-444-4-4-44-200002-22-2-22200000000000−232323−2300000002i2−2i200000000−i2i2i2−i2−i6i6i6−i6000000000000000000000000
χ744-44-444-4-440000-44-4-4-44400000000000000000000000000000000000000004i−4i0000000000000000000000
χ754-44-444-4-440000-44-4-4-4440000000000000000000000000000000000000000−4i4i0000000000000000000000
χ764-4-444-44-44-44-44-4-44-444-400000000-4-4400004000000000000000000000000000000000000000000000000
χ774-4-444-44-4-24-44-422-22-2-224i−4i4i−4i0000-2-2200002000000000000−2i2i−2i2i00000000000000000000000000000000
χ784-4-444-44-4-24-44-422-22-2-22−4i4i−4i4i0000-2-22000020000000000002i−2i2i−2i00000000000000000000000000000000
χ794-4-444-44-4-2-44-4422-22-2-220000000022-20000-200−2i32i32i3−2i3000000000000000000000000000000000000000000
χ804-4-444-44-4-2-44-4422-22-2-220000000022-20000-2002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ814-4-4-4-4444-244-4-422-2-222-200004-44-42-22-2-222-20000000000-22000000000000000000000000000000000000
χ824-4-4-4-4444-244-4-422-2-222-20000-44-442-2222-2-2-200000000002-2000000000000000000000000000000000000
χ8388-88-88-8-8-40000-4444-44-40000000000000000000000000000000000000000000000000000000000000000
χ848-88-888-8-8-400004-4444-4-40000000000000000000000000000000000000000000000000000000000000000

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