Finite Group Databasebeta

← Group #10828809

Character table — Group #10828809

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444444444444444444444448888121212121212121216161616161616161616242424242424242424242424
order122222223444444446666666226666888888881212121212121212242424242424242424242424242424242244444444444466121212121212244444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-11-1-1111-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-11111
χ91111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11-111-1-111-1-1111-111-1-111-1-1
χ101111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-11111111-111-1-111-1-1-1-1-11-1-111-1-111
χ111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-11-1-111-1-1111-1-1-1-1-11111-1-1
χ121111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-11-1-111-1-111-111111-1-1-1-111
χ131111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1111-1-1-1-1111-1-1-11111-1-111
χ141111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1111-1-1-1-111-1111-1-1-1-111-1-1
χ151111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-111111-1-1-11111-1-1111-1-1-1-1-1-1-111
χ161111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11-1-1-11111-1-1-1-1-11111111-1-1
χ17222222222-22222-2-2-22222222-2-2-2-2-2-200000000-2-2-22222-200000000000000000000222200000000000000-200-200000000
χ18222222222-22222-2-2-22222222-2-2-2-2-2-200000000-2-2-22222-200000000000000000000-2-2-2-200000000000000200200000000
χ19222222222-2-2-2-2-2-2-2-2222222222222200000000-2-2-2-2-2-2-2-20000000000000000000022-2-200000000000000-200200000000
χ20222222222-2-2-2-2-2-2-2-2222222222222200000000-2-2-2-2-2-2-2-200000000000000000000-2-22200000000000000200-200000000
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000000022-1-1-1-1-1-1-1-1000000000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-211111111000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111222200000000-2-2-1-1-1-11111000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-200000000221111-1-1-1-1000000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-211112222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-11111111122-2-2000000002-2-1-111-1-111000000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-211112222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-111111111-2-22200000000-2211-1-111-1-1000000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-21111-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-122-2-200000000-22-1-11111-1-1000000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-21111-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-1-2-222000000002-211-1-1-1-111000000000000
χ2922-22-22-2-22-2000022-22-2-222-2-2000000000022-2-22-2-200002000000002222-2-2-2-2000000002i2i−2i−2i000000000002i−2i000000000
χ3022-22-22-2-22-2000022-22-2-222-2-2000000000022-2-22-2-200002000000002222-2-2-2-200000000−2i−2i2i2i00000000000−2i2i000000000
χ3122-22-22-2-22-2000022-22-2-222-2-20000000000-2-2222-2-20000200000000-2-2-2-22222000000002i2i−2i−2i00000000000−2i2i000000000
χ3222-22-22-2-22-2000022-22-2-222-2-20000000000-2-2222-2-20000200000000-2-2-2-2222200000000−2i−2i2i2i000000000002i−2i000000000
χ332-222-2-22-2202i2i−2i−2i000-2222-2-2-2000000−i2−i2i2i22−22−20002i2i−2i−2i0−i2−i2−i2−i2i2i2i2i222−2−222−2−200002i−2i2-200000000000000000000002−2−i2i2
χ342-222-2-22-2202i2i−2i−2i000-2222-2-2-2000000−i2−i2i2i22−22−20002i2i−2i−2i0−i2−i2−i2−i2i2i2i2i222−2−222−2−20000−2i2i-220000000000000000000000−22i2−i2
χ352-222-2-22-2202i2i−2i−2i000-2222-2-2-2000000i2i2−i2−i2−22−220002i2i−2i−2i0i2i2i2i2−i2−i2−i2−i2−2−222−2−22200002i−2i2-20000000000000000000000−22i2−i2
χ362-222-2-22-2202i2i−2i−2i000-2222-2-2-2000000i2i2−i2−i2−22−220002i2i−2i−2i0i2i2i2i2−i2−i2−i2−i2−2−222−2−2220000−2i2i-2200000000000000000000002−2−i2i2
χ372-222-2-22-220−2i−2i2i2i000-2222-2-2-2000000−i2−i2i2i2−22−22000−2i−2i2i2i0−i2−i2−i2−i2i2i2i2i2−2−222−2−22200002i−2i-2200000000000000000000002−2i2−i2
χ382-222-2-22-220−2i−2i2i2i000-2222-2-2-2000000−i2−i2i2i2−22−22000−2i−2i2i2i0−i2−i2−i2−i2i2i2i2i2−2−222−2−2220000−2i2i2-20000000000000000000000−22−i2i2
χ392-222-2-22-220−2i−2i2i2i000-2222-2-2-2000000i2i2−i2−i22−22−2000−2i−2i2i2i0i2i2i2i2−i2−i2−i2−i222−2−222−2−200002i−2i-220000000000000000000000−22−i2i2
χ402-222-2-22-220−2i−2i2i2i000-2222-2-2-2000000i2i2−i2−i22−22−2000−2i−2i2i2i0i2i2i2i2−i2−i2−i2−i222−2−222−2−20000−2i2i2-200000000000000000000002−2i2−i2
χ412-22-222-2-22-200002-22-22-2-222-20000002-22-20000-22-20000222-2-222-2-200000000000000002i−2i2i−2i00000000000000002i−2i0000
χ422-22-222-2-22-200002-22-22-2-222-20000002-22-20000-22-20000222-2-222-2-20000000000000000−2i2i−2i2i0000000000000000−2i2i0000
χ432-22-222-2-22-200002-22-22-2-222-2000000-22-220000-22-200002-2-222-2-22200000000000000002i−2i2i−2i0000000000000000−2i2i0000
χ442-22-222-2-22-200002-22-22-2-222-2000000-22-220000-22-200002-2-222-2-2220000000000000000−2i2i−2i2i00000000000000002i−2i0000
χ452-2-2-2-2222222-22-22-2-2-2-22-22-222-222-2-200000000-2-222-22-220000000000000000000000002-2-22000000000000002-2000000
χ462-2-2-2-2222222-22-22-2-2-2-22-22-222-222-2-200000000-2-222-22-22000000000000000000000000-222-200000000000000-22000000
χ472-2-2-2-222222-22-222-2-2-2-22-22-22-22-2-22200000000-2-22-22-2220000000000000000000000002-2-2200000000000000-22000000
χ482-2-2-2-222222-22-222-2-2-2-22-22-22-22-2-22200000000-2-22-22-222000000000000000000000000-222-2000000000000002-2000000
χ492-2-2-2-22222-22-22-2-222-2-22-22-22-22-2-2220000000022-22-22-2-200000000000000002-22-200000000002-22-20000000000000000
χ502-2-2-2-22222-22-22-2-222-2-22-22-22-22-2-2220000000022-22-22-2-20000000000000000-22-220000000000-22-220000000000000000
χ512-2-2-2-22222-2-22-22-222-2-22-22-222-222-2-20000000022-2-22-22-200000000000000002-2-2200000000002-2-220000000000000000
χ522-2-2-2-22222-2-22-22-222-2-22-22-222-222-2-20000000022-2-22-22-20000000000000000-222-20000000000-222-20000000000000000
χ532-2-2-2-2222-1-22-22-2-22211-11-11-1-2211-1-100000000-1-11-11-1113−33−33−33−33−33−33−33−32-22-20000000000-11-113−33−3000000000000
χ542-2-2-2-2222-1-22-22-2-22211-11-11-1-2211-1-100000000-1-11-11-1113−33−33−33−33−33−33−33−3-22-2200000000001-11-1−33−33000000000000
χ552-2-2-2-2222-1-22-22-2-22211-11-11-1-2211-1-100000000-1-11-11-111−33−33−33−33−33−33−33−332-22-20000000000-11-11−33−33000000000000
χ562-2-2-2-2222-1-22-22-2-22211-11-11-1-2211-1-100000000-1-11-11-111−33−33−33−33−33−33−33−33-22-2200000000001-11-13−33−3000000000000
χ572-2-2-2-2222-1-2-22-22-22211-11-11-12-2-1-11100000000-1-111-11-113−33−33−33−3−33−33−33−332-2-220000000000-111-13−3−33000000000000
χ582-2-2-2-2222-1-2-22-22-22211-11-11-12-2-1-11100000000-1-111-11-113−33−33−33−3−33−33−33−33-222-200000000001-1-11−333−3000000000000
χ592-2-2-2-2222-1-2-22-22-22211-11-11-12-2-1-11100000000-1-111-11-11−33−33−33−333−33−33−33−32-2-220000000000-111-1−333−3000000000000
χ602-2-2-2-2222-1-2-22-22-22211-11-11-12-2-1-11100000000-1-111-11-11−33−33−33−333−33−33−33−3-222-200000000001-1-113−3−33000000000000
χ6144444444-2-44444-4-4-4-2-2-2-2-2-2-2-4-4222200000000222-2-2-2-2200000000000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-244-2-2-2-2000000002222222200000000000000000000000000000000000000000000000000
χ63444-4-4-4-4440000000044-4-4-4-44000000−2i22i22i2−2i2000000000000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ64444-4-4-4-4440000000044-4-4-4-440000002i2−2i2−2i22i20000000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ65444-4-4-4-44-200000000-2-22222-200−2i32i3−2i32i3−2i22i22i2−2i2000000000000i2i2−i2−i2−i2−i2i2i26−6−66−666−60000000000000000000000000000000000
χ66444-4-4-4-44-200000000-2-22222-200−2i32i3−2i32i32i2−2i2−2i22i2000000000000−i2−i2i2i2i2i2−i2−i2−666−66−6−660000000000000000000000000000000000
χ67444-4-4-4-44-200000000-2-22222-2002i3−2i32i3−2i3−2i22i22i2−2i2000000000000i2i2−i2−i2−i2−i2i2i2−666−66−6−660000000000000000000000000000000000
χ68444-4-4-4-44-200000000-2-22222-2002i3−2i32i3−2i32i2−2i2−2i22i2000000000000−i2−i2i2i2i2i2−i2−i26−6−66−666−60000000000000000000000000000000000
χ6944-44-44-4-4440000-4-444-4-444-4-400000000000000-4440000-400000000000000000000000000000000000000000000000000
χ7044-44-44-4-4-240000-4-44-222-2-222000000000000002-2-20000223−23−232323−23−2323000000000000000000000000000000000000000000
χ7144-44-44-4-4-240000-4-44-222-2-222000000000000002-2-200002−232323−23−232323−23000000000000000000000000000000000000000000
χ7244-44-44-4-4-2-4000044-4-222-2-222000000000044-4-4-2220000-200000000-2-2-2-222220000000000000000000000000000000000
χ7344-44-44-4-4-2-4000044-4-222-2-2220000000000-4-444-2220000-2000000002222-2-2-2-20000000000000000000000000000000000
χ7444-4-44-44-4404i−4i−4i4i0004-44-4-44-4000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000000
χ7544-4-44-44-440−4i4i4i−4i0004-44-4-44-400000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ7644-4-44-44-4-204i−4i−4i4i000-22-222-2200000000000000000−2i2i2i−2i0i6−i6i6−i6−i6i6−i6i6−666−6−666−60000000000000000000000000000000000
χ7744-4-44-44-4-204i−4i−4i4i000-22-222-2200000000000000000−2i2i2i−2i0−i6i6−i6i6i6−i6i6−i66−6−666−6−660000000000000000000000000000000000
χ7844-4-44-44-4-20−4i4i4i−4i000-22-222-22000000000000000002i−2i−2i2i0i6−i6i6−i6−i6i6−i6i66−6−666−6−660000000000000000000000000000000000
χ7944-4-44-44-4-20−4i4i4i−4i000-22-222-22000000000000000002i−2i−2i2i0−i6i6−i6i6i6−i6i6−i6−666−6−666−60000000000000000000000000000000000
χ804-444-4-44-4-204i4i−4i−4i0002-2-2-2222000000−2i2−2i22i22i222−2222−22000−2i−2i2i2i0i2i2i2i2−i2−i2−i2−i2−2−222−2−2220000000000000000000000000000000000
χ814-444-4-44-4-204i4i−4i−4i0002-2-2-22220000002i22i2−2i2−2i2−2222−2222000−2i−2i2i2i0−i2−i2−i2−i2i2i2i2i222−2−222−2−20000000000000000000000000000000000
χ824-444-4-44-4-20−4i−4i4i4i0002-2-2-2222000000−2i2−2i22i22i2−2222−22220002i2i−2i−2i0i2i2i2i2−i2−i2−i2−i222−2−222−2−20000000000000000000000000000000000
χ834-444-4-44-4-20−4i−4i4i4i0002-2-2-22220000002i22i2−2i2−2i222−2222−220002i2i−2i−2i0−i2−i2−i2−i2i2i2i2i2−2−222−2−2220000000000000000000000000000000000
χ844-44-444-4-4440000-44-4-44-4-444-4000000000000004-440000-400000000000000000000000000000000000000000000000000
χ854-44-444-4-4-240000-44-42-222-2-2200000000000000-22-2000020000000023−2323−23−2323−23230000000000000000000000000000000000
χ864-44-444-4-4-240000-44-42-222-2-2200000000000000-22-20000200000000−2323−232323−2323−230000000000000000000000000000000000
χ874-44-444-4-4-2-400004-442-222-2-220000004-44-400002-220000-2-2-222-2-222000000000000000000000000000000000000000000
χ884-44-444-4-4-2-400004-442-222-2-22000000-44-4400002-220000-222-2-222-2-2000000000000000000000000000000000000000000
χ894-4-444-4-44400000000-4-4-44-444000000000022−22−222200000000000000002222−22−22−22−2222220000000000000000000000000000000000
χ904-4-444-4-44400000000-4-4-44-4440000000000−222222−220000000000000000−22−2222222222−22−220000000000000000000000000000000000
χ914-4-444-4-44-200000000222-22-2-200−2i32i32i3−2i3000022−22−222200000000−i6i6i6−i6i6−i6−i6i6−2−22222−2−20000000000000000000000000000000000
χ924-4-444-4-44-200000000222-22-2-200−2i32i32i3−2i30000−222222−2200000000i6−i6−i6i6−i6i6i6−i622−2−2−2−2220000000000000000000000000000000000
χ934-4-444-4-44-200000000222-22-2-2002i3−2i3−2i32i3000022−22−222200000000i6−i6−i6i6−i6i6i6−i6−2−22222−2−20000000000000000000000000000000000
χ944-4-444-4-44-200000000222-22-2-2002i3−2i3−2i32i30000−222222−2200000000−i6i6i6−i6i6−i6−i6i622−2−2−2−2220000000000000000000000000000000000
χ954-4-4-4-4444-244-44-44-4-422-22-22-24-4-2-2220000000022-2-22-22-200000000000000000000000000000000000000000000000000
χ964-4-4-4-4444-24-44-444-4-422-22-22-2-4422-2-20000000022-22-22-2-200000000000000000000000000000000000000000000000000

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