Finite Group Databasebeta

← Group #10846053

Character table — Group #10846053

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order1222222234444666666622446666888888881212121212121212242424242424242424242424242424242244444424666612121212244444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1111-1-111-1-111-1-111-1-1-1-1-11
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-111-1-1-1-111-1-111111-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-111-1-1111111-1-1-1-1-1-11-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-111-1-111-1-1-1-1111111-11
χ911111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1111111-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111
χ1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111111-11111-1-1-1-1-1-1-1-111-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11-11111-1-1-1-11111-1-111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1111111-11-1-1-1-11111-1-111-1-1-1-111-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-11-1-1-1-1111111-1-11111-1-11-1
χ17222222222-2-2-2-2222222222-2-2222200000000-2-2-2-2-2-2-2-20000000000000000000022-2-200000000002-20000000000
χ18222222222-2-2-2-2222222222-2-2222200000000-2-2-2-2-2-2-2-200000000000000000000-2-2220000000000-220000000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-200000000-2-2-22222-20000000000000000000022-2-20000000000-220000000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-200000000-2-2-22222-200000000000000000000-2-22200000000002-20000000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000022-1-1-1-1-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-211111111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-20000-22-1-111-1-111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-22200002-211-1-111-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-211112222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-11111111122220000-2-2-1-11111-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-211112222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-111111111-2-2-2-200002211-1-1-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-122-2-200002-2-1-1-1-11111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-1-2-2220000-221111-1-1-1-1000000000000
χ2922-2-222-2-222-22-222-2-2-22-2000000002i2i−2i−2i000022-20000-22i2i2i2i−2i−2i−2i−2i00000000000000000000000000002-22i−2i000000
χ3022-2-222-2-222-22-222-2-2-22-2000000002i2i−2i−2i000022-20000-22i2i2i2i−2i−2i−2i−2i0000000000000000000000000000-22−2i2i000000
χ3122-2-222-2-222-22-222-2-2-22-200000000−2i−2i2i2i000022-20000-2−2i−2i−2i−2i2i2i2i2i00000000000000000000000000002-2−2i2i000000
χ3222-2-222-2-222-22-222-2-2-22-200000000−2i−2i2i2i000022-20000-2−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000-222i−2i000000
χ332-22-22-2-22222-2-2-2-222-22-2000000002i−2i2i−2i00002-220000-22i2i−2i−2i2i2i−2i−2i0000000000002-22-200000000000000002i−2i0000
χ342-22-22-2-22222-2-2-2-222-22-2000000002i−2i2i−2i00002-220000-22i2i−2i−2i2i2i−2i−2i000000000000-22-220000000000000000−2i2i0000
χ352-22-22-2-22222-2-2-2-222-22-200000000−2i2i−2i2i00002-220000-2−2i−2i2i2i−2i−2i2i2i0000000000002-22-20000000000000000−2i2i0000
χ362-22-22-2-22222-2-2-2-222-22-200000000−2i2i−2i2i00002-220000-2−2i−2i2i2i−2i−2i2i2i000000000000-22-2200000000000000002i−2i0000
χ372-22-22-2-222-2-222-2-222-22-200000000000022-2-2-22-200002000000002222-2-2-2-200002-2-220000000000000000002-200
χ382-22-22-2-222-2-222-2-222-22-200000000000022-2-2-22-200002000000002222-2-2-2-20000-222-2000000000000000000-2200
χ392-22-22-2-222-2-222-2-222-22-2000000000000-2-222-22-20000200000000-2-2-2-2222200002-2-22000000000000000000-2200
χ402-22-22-2-222-2-222-2-222-22-2000000000000-2-222-22-20000200000000-2-2-2-222220000-222-20000000000000000002-200
χ412-2-222-22-222-2-22-2-2-2-2222000000002-2-2200002-2-20000222-2-2-2-222000000002-22-20000002-200002-2000000000000
χ422-2-222-22-222-2-22-2-2-2-2222000000002-2-2200002-2-20000222-2-2-2-22200000000-22-22000000-220000-22000000000000
χ432-2-222-22-222-2-22-2-2-2-222200000000-222-200002-2-200002-2-22222-2-2000000002-2-220000002-20000-22000000000000
χ442-2-222-22-222-2-22-2-2-2-222200000000-222-200002-2-200002-2-22222-2-200000000-222-2000000-2200002-2000000000000
χ452-2-222-22-2-12-2-221111-1-1-10000−i3−i3i3i32-2-220000-111−i3−i3i3i3-1-1-11111-1-1−i3−i3i3i3−i3−i3i3i32-22-2000000-11−i3i3−i3i3-11000000000000
χ462-2-222-22-2-12-2-221111-1-1-10000−i3−i3i3i32-2-220000-111−i3−i3i3i3-1-1-11111-1-1−i3−i3i3i3−i3−i3i3i3-22-220000001-1i3−i3i3−i31-1000000000000
χ472-2-222-22-2-12-2-221111-1-1-10000−i3−i3i3i3-222-20000-111−i3−i3i3i3-111-1-1-1-111i3i3−i3−i3i3i3−i3−i32-2-22000000-11i3−i3−i3i31-1000000000000
χ482-2-222-22-2-12-2-221111-1-1-10000−i3−i3i3i3-222-20000-111−i3−i3i3i3-111-1-1-1-111i3i3−i3−i3i3i3−i3−i3-222-20000001-1−i3i3i3−i3-11000000000000
χ492-2-222-22-2-12-2-221111-1-1-10000i3i3−i3−i32-2-220000-111i3i3−i3−i3-1-1-11111-1-1i3i3−i3−i3i3i3−i3−i32-22-2000000-11i3−i3i3−i3-11000000000000
χ502-2-222-22-2-12-2-221111-1-1-10000i3i3−i3−i32-2-220000-111i3i3−i3−i3-1-1-11111-1-1i3i3−i3−i3i3i3−i3−i3-22-220000001-1−i3i3−i3i31-1000000000000
χ512-2-222-22-2-12-2-221111-1-1-10000i3i3−i3−i3-222-20000-111i3i3−i3−i3-111-1-1-1-111−i3−i3i3i3−i3−i3i3i32-2-22000000-11−i3i3i3−i31-1000000000000
χ522-2-222-22-2-12-2-221111-1-1-10000i3i3−i3−i3-222-20000-111i3i3−i3−i3-111-1-1-1-111−i3−i3i3i3−i3−i3i3i3-222-20000001-1i3−i3−i3i3-11000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4-2-2-2-200000000222222220000000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444222200000000222-2-2-2-220000000000000000000000000000000000000000000000
χ55444-4-4-44-4400004-44-44-4-4004i−4i0000000000000004i−4i4i−4i00000000000000000000000000000000000000000000000
χ56444-4-4-44-4400004-44-44-4-400−4i4i000000000000000−4i4i−4i4i00000000000000000000000000000000000000000000000
χ57444-4-4-44-4-20000-22-22-222004i−4i000000000000000−2i2i−2i2i06−66−66−66−6i6−i6i6−i6i6−i6i6−i6000000000000000000000000000000
χ58444-4-4-44-4-20000-22-22-222004i−4i000000000000000−2i2i−2i2i0−66−66−66−66−i6i6−i6i6−i6i6−i6i6000000000000000000000000000000
χ59444-4-4-44-4-20000-22-22-22200−4i4i0000000000000002i−2i2i−2i06−66−66−66−6−i6i6−i6i6−i6i6−i6i6000000000000000000000000000000
χ60444-4-4-44-4-20000-22-22-22200−4i4i0000000000000002i−2i2i−2i0−66−66−66−66i6−i6i6−i6i6−i6i6−i6000000000000000000000000000000
χ6144-44-4-4-44400004-4-44-4-4400000000000022−2222−22000000000000000022−22−2222−222222−22000000000000000000000000000000
χ6244-44-4-4-44400004-4-44-4-44000000000000−2222−22220000000000000000−222222−2222−22−2222000000000000000000000000000000
χ6344-44-4-4-44-20000-222-222-20000−2i32i3−2i32i3000022−2222−2200000000i6−i6i6−i6−i6i6−i6i6−222−22−2−22000000000000000000000000000000
χ6444-44-4-4-44-20000-222-222-20000−2i32i3−2i32i30000−2222−222200000000−i6i6−i6i6i6−i6i6−i62−2−22−222−2000000000000000000000000000000
χ6544-44-4-4-44-20000-222-222-200002i3−2i32i3−2i3000022−2222−2200000000−i6i6−i6i6i6−i6i6−i6−222−22−2−22000000000000000000000000000000
χ6644-44-4-4-44-20000-222-222-200002i3−2i32i3−2i30000−2222−222200000000i6−i6i6−i6−i6i6−i6i62−2−22−222−2000000000000000000000000000000
χ6744-4-444-4-44-44-4444-4-4-44-40000000000000000-4-44000040000000000000000000000000000000000000000000000
χ6844-4-444-4-4-24-44-4-2-2222-22000000004i4i−4i−4i0000-2-2200002−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000000000
χ6944-4-444-4-4-24-44-4-2-2222-2200000000−4i−4i4i4i0000-2-22000022i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000000000
χ7044-4-444-4-4-2-44-44-2-2222-22000000000000000022-20000-200000000−2i3−2i32i32i32i32i3−2i3−2i3000000000000000000000000000000
χ7144-4-444-4-4-2-44-44-2-2222-22000000000000000022-20000-2000000002i32i3−2i3−2i3−2i3−2i32i32i3000000000000000000000000000000
χ724-444-44-4-440000-444-4-4-444-4004-4-4400000000000000000000000000000000000000000000000000000000000000
χ734-444-44-4-440000-444-4-4-44-4400-444-400000000000000000000000000000000000000000000000000000000000000
χ744-444-44-4-4-200002-2-2222-24-400-222-20000000000000000i6−i6−i6i6i6−i6−i6i6−i6i6−i6i6i6−i6i6−i6000000000000000000000000000000
χ754-444-44-4-4-200002-2-2222-24-400-222-20000000000000000−i6i6i6−i6−i6i6i6−i6i6−i6i6−i6−i6i6−i6i6000000000000000000000000000000
χ764-444-44-4-4-200002-2-2222-2-44002-2-220000000000000000i6−i6−i6i6i6−i6−i6i6i6−i6i6−i6−i6i6−i6i6000000000000000000000000000000
χ774-444-44-4-4-200002-2-2222-2-44002-2-220000000000000000−i6i6i6−i6−i6i6i6−i6−i6i6−i6i6i6−i6i6−i6000000000000000000000000000000
χ784-44-44-4-44-244-4-422-2-22-22000000004i−4i4i−4i0000-22-200002−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000
χ794-44-44-4-44-244-4-422-2-22-2200000000−4i4i−4i4i0000-22-2000022i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000
χ804-44-44-4-44-2-4-44422-2-22-2200000000000044-4-42-220000-200000000-2-2-2-22222000000000000000000000000000000
χ814-44-44-4-44-2-4-44422-2-22-22000000000000-4-4442-220000-2000000002222-2-2-2-2000000000000000000000000000000
χ824-4-444-44-44-444-4-4-4-4-44440000000000000000-4440000-40000000000000000000000000000000000000000000000
χ834-4-444-44-4-2-444-42222-2-2-20000−2i3−2i32i32i3000000002-2-22i32i3−2i3−2i320000000000000000000000000000000000000000000000
χ844-4-444-44-4-2-444-42222-2-2-200002i32i3−2i3−2i3000000002-2-2−2i3−2i32i32i320000000000000000000000000000000000000000000000
χ854-4-4-4-444440000-44-444-4-400000000000022−22−2222000000000000000022−22−222222−22−2222000000000000000000000000000000
χ864-4-4-4-444440000-44-444-4-4000000000000−222222−220000000000000000−222222−22−222222−22000000000000000000000000000000
χ874-4-4-4-4444-200002-22-2-22200000000000022−22−222200023−23−23230−666−66−6−66−222−2−222−2000000000000000000000000000000
χ884-4-4-4-4444-200002-22-2-22200000000000022−22−2222000−232323−2306−6−66−666−6−222−2−222−2000000000000000000000000000000
χ894-4-4-4-4444-200002-22-2-222000000000000−222222−2200023−23−232306−6−66−666−62−2−222−2−22000000000000000000000000000000
χ904-4-4-4-4444-200002-22-2-222000000000000−222222−22000−232323−230−666−66−6−662−2−222−2−22000000000000000000000000000000

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