Finite Group Databasebeta

← Group #10827337

Character table — Group #10827337

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444444444444444444444448888121212121212121216161616161616161616242424242424242424242424
order122222222222344446666666446666888888881212121212121212242424242424242424242424242424242244224444444466121212121212222244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1111111
χ911111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11-111-1-111-1-111-1-1-111111-1-1
χ1011111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-11111111-111-1-111-1-1-1-1111-1-1-1-1-111
χ1111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-11-1-111-1-111-1-111-11-1-111-1-1
χ1211111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-11-1-111-1-11111-1-11-111-1-111
χ1311111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1111-1-1-1-111-1-111-1111-1-111
χ1411111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1111-1-1-1-11111-1-11-1-1-111-1-1
χ1511111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-111111-1-1-11111-1-111-1-1-11-1-1-1-111
χ1611111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11-1-1-11111-1-1-1-1111-11111-1-1
χ172222222222222-2-2-2-22222222-2-2222200000000-2-2-2-2-2-2-2-2000000000000000000002222000000000000000000-2-2000000
χ182222222222222-2-2-2-22222222-2-2222200000000-2-2-2-2-2-2-2-200000000000000000000-2-2-2-200000000000000000022000000
χ19222222222222-12222-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000000022-1-1-1-1-1-1-1-1000000000000
χ20222222222222-12222-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-211111111000000000000
χ21222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111222200000000-2-2-1-1-1-11111000000000000
χ22222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-200000000221111-1-1-1-1000000000000
χ2322222222-2-2-2-22-2-2-2-2222222222-2-2-2-200000000-2-2-22222-20000000000000000000022-2-20000000000000000002-2000000
χ2422222222-2-2-2-22-2-2-2-2222222222-2-2-2-200000000-2-2-22222-200000000000000000000-2-222000000000000000000-22000000
χ2522222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-211112222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-11111111122-2-2000000002-2-1-111-1-111000000000000
χ2622222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-211112222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-111111111-2-22200000000-2211-1-111-1-1000000000000
χ2722222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-122-2-200000000-22-1-11111-1-1000000000000
χ2822222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-1-2-222000000002-211-1-1-1-111000000000000
χ2922-22-2-22-2000022-22-22-2-222-2-200000000002i2i−2i−2i22-20000-2000000002i2i2i2i−2i−2i−2i−2i000000002i2i−2i−2i00000000002-20000000000
χ3022-22-2-22-2000022-22-22-2-222-2-200000000002i2i−2i−2i22-20000-2000000002i2i2i2i−2i−2i−2i−2i00000000−2i−2i2i2i0000000000-220000000000
χ3122-22-2-22-2000022-22-22-2-222-2-20000000000−2i−2i2i2i22-20000-200000000−2i−2i−2i−2i2i2i2i2i000000002i2i−2i−2i0000000000-220000000000
χ3222-22-2-22-2000022-22-22-2-222-2-20000000000−2i−2i2i2i22-20000-200000000−2i−2i−2i−2i2i2i2i2i00000000−2i−2i2i2i00000000002-20000000000
χ332-22-22-22-2000022-2-22-22-22-22-20000002i2i−2i−2i00002-220000-22i2i2i2i−2i−2i−2i−2i00000000000000002i−2i2i−2i0000000000002-200000000
χ342-22-22-22-2000022-2-22-22-22-22-20000002i2i−2i−2i00002-220000-22i2i2i2i−2i−2i−2i−2i0000000000000000−2i2i−2i2i000000000000-2200000000
χ352-22-22-22-2000022-2-22-22-22-22-2000000−2i−2i2i2i00002-220000-2−2i−2i−2i−2i2i2i2i2i00000000000000002i−2i2i−2i000000000000-2200000000
χ362-22-22-22-2000022-2-22-22-22-22-2000000−2i−2i2i2i00002-220000-2−2i−2i−2i−2i2i2i2i2i0000000000000000−2i2i−2i2i0000000000002-200000000
χ372-2-222-2-2222-2-220000-2-2-2-22220022-2-22−22−22−22−20000000022−2−222−2−222−2−222−2−200002-22-200000000000000000000002−22−2
χ382-2-222-2-2222-2-220000-2-2-2-22220022-2-22−22−22−22−20000000022−2−222−2−222−2−222−2−20000-22-220000000000000000000000−22−22
χ392-2-222-2-2222-2-220000-2-2-2-22220022-2-2−22−22−22−2200000000−2−222−2−222−2−222−2−22200002-22-20000000000000000000000−22−22
χ402-2-222-2-2222-2-220000-2-2-2-22220022-2-2−22−22−22−2200000000−2−222−2−222−2−222−2−2220000-22-2200000000000000000000002−22−2
χ412-2-222-2-22-2-22220000-2-2-2-222200-2-2222−22−2−22−220000000022−2−222−2−2−2−222−2−22200002-2-2200000000000000000000002−2−22
χ422-2-222-2-22-2-22220000-2-2-2-222200-2-2222−22−2−22−220000000022−2−222−2−2−2−222−2−2220000-222-20000000000000000000000−222−2
χ432-2-222-2-22-2-22220000-2-2-2-222200-2-222−22−222−22−200000000−2−222−2−22222−2−222−2−200002-2-220000000000000000000000−222−2
χ442-2-222-2-22-2-22220000-2-2-2-222200-2-222−22−222−22−200000000−2−222−2−22222−2−222−2−20000-222-200000000000000000000002−2−22
χ452-2-2-2-22222-22-2222-2-2-2-222-2-222-22-22-2000000002-2-222-2-220000000000000000000000002-2-2200000000000000002-20000
χ462-2-2-2-22222-22-2222-2-2-2-222-2-222-22-22-2000000002-2-222-2-22000000000000000000000000-222-20000000000000000-220000
χ472-2-2-2-22222-22-22-2-222-2-222-2-22-222-22-200000000-222-2-222-200000000000000002-22-200000000002-22-20000000000000000
χ482-2-2-2-22222-22-22-2-222-2-222-2-22-222-22-200000000-222-2-222-20000000000000000-22-220000000000-22-220000000000000000
χ492-2-2-2-22222-22-2-1-2-22211-1-111-1-22-11-11000000001-1-111-1-113−33−33−33−33−33−33−33−32-22-20000000000-11-113−33−3000000000000
χ502-2-2-2-22222-22-2-1-2-22211-1-111-1-22-11-11000000001-1-111-1-113−33−33−33−33−33−33−33−3-22-2200000000001-11-1−33−33000000000000
χ512-2-2-2-22222-22-2-1-2-22211-1-111-1-22-11-11000000001-1-111-1-11−33−33−33−33−33−33−33−332-22-20000000000-11-11−33−33000000000000
χ522-2-2-2-22222-22-2-1-2-22211-1-111-1-22-11-11000000001-1-111-1-11−33−33−33−33−33−33−33−33-22-2200000000001-11-13−33−3000000000000
χ532-2-2-2-2222-22-22222-2-2-2-222-2-22-22-22-22000000002-2-2-2-22220000000000000000000000002-2-220000000000000000-220000
χ542-2-2-2-2222-22-22222-2-2-2-222-2-22-22-22-22000000002-2-2-2-2222000000000000000000000000-222-200000000000000002-20000
χ552-2-2-2-2222-22-222-2-222-2-222-2-222-2-22-2200000000-22222-2-2-200000000000000002-2-2200000000002-2-220000000000000000
χ562-2-2-2-2222-22-222-2-222-2-222-2-222-2-22-2200000000-22222-2-2-20000000000000000-222-20000000000-222-20000000000000000
χ572-2-2-2-2222-22-22-1-2-22211-1-111-12-21-11-1000000001-1-1-1-11113−33−33−33−3−33−33−33−332-2-220000000000-111-13−3−33000000000000
χ582-2-2-2-2222-22-22-1-2-22211-1-111-12-21-11-1000000001-1-1-1-11113−33−33−33−3−33−33−33−33-222-200000000001-1-11−333−3000000000000
χ592-2-2-2-2222-22-22-1-2-22211-1-111-12-21-11-1000000001-1-1-1-1111−33−33−33−333−33−33−33−32-2-220000000000-111-1−333−3000000000000
χ602-2-2-2-2222-22-22-1-2-22211-1-111-12-21-11-1000000001-1-1-1-1111−33−33−33−333−33−33−33−3-222-200000000001-1-113−3−33000000000000
χ61444444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4-2-2-2-2000000002222222200000000000000000000000000000000000000000000000000
χ6244444444-4-4-4-4-2-4-4-4-4-2-2-2-2-2-2-244222200000000222-2-2-2-2200000000000000000000000000000000000000000000000000
χ63444-4-4-4-444-4-444000044-4-4-4-44004-4-44000000000000000000000000000000000000000000000000000000000000000000
χ64444-4-4-4-444-4-44-20000-2-22222-200-222-200000000000000006−6−666−6−666−6−666−6−660000000000000000000000000000000000
χ65444-4-4-4-444-4-44-20000-2-22222-200-222-20000000000000000−666−6−666−6−666−6−666−60000000000000000000000000000000000
χ66444-4-4-4-44-444-44000044-4-4-4-4400-444-4000000000000000000000000000000000000000000000000000000000000000000
χ67444-4-4-4-44-444-4-20000-2-22222-2002-2-2200000000000000006−6−666−6−66−666−6−666−60000000000000000000000000000000000
χ68444-4-4-4-44-444-4-20000-2-22222-2002-2-220000000000000000−666−6−666−66−6−666−6−660000000000000000000000000000000000
χ6944-44-4-44-400004-44-444-4-444-4-400000000000000-4-440000400000000000000000000000000000000000000000000000000
χ7044-44-4-44-40000-24-44-4-222-2-22200000000004i4i−4i−4i-2-220000200000000−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000
χ7144-44-4-44-40000-24-44-4-222-2-2220000000000−4i−4i4i4i-2-2200002000000002i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000
χ7244-44-4-44-40000-2-44-44-222-2-2220000000000000022-20000-2−2i32i3−2i32i32i3−2i32i3−2i3000000000000000000000000000000000000000000
χ7344-44-4-44-40000-2-44-44-222-2-2220000000000000022-20000-22i3−2i32i3−2i3−2i32i3−2i32i3000000000000000000000000000000000000000000
χ7444-4-444-4-40000400004-44-4-44-4000000−2i22i22i2−2i2000000000000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ7544-4-444-4-40000400004-44-4-44-40000002i2−2i2−2i22i20000000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ7644-4-444-4-40000-20000-22-222-22000000−2i22i22i2−2i2000000023−2323−230i2i2−i2−i2−i2−i2i2i2i6−i6−i6i6−i6i6i6−i60000000000000000000000000000000000
χ7744-4-444-4-40000-20000-22-222-22000000−2i22i22i2−2i20000000−2323−23230i2i2−i2−i2−i2−i2i2i2−i6i6i6−i6i6−i6−i6i60000000000000000000000000000000000
χ7844-4-444-4-40000-20000-22-222-220000002i2−2i2−2i22i2000000023−2323−230−i2−i2i2i2i2i2−i2−i2−i6i6i6−i6i6−i6−i6i60000000000000000000000000000000000
χ7944-4-444-4-40000-20000-22-222-220000002i2−2i2−2i22i20000000−2323−23230−i2−i2i2i2i2i2−i2−i2i6−i6−i6i6−i6i6i6−i60000000000000000000000000000000000
χ804-444-44-4-4000040000-444-44-4-40000000000−2i22i22i2−2i20000000000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ814-444-44-4-4000040000-444-44-4-400000000002i2−2i2−2i22i200000000000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ824-444-44-4-40000-200002-2-22-2220000000000−2i22i22i2−2i200023−23−23230i6−i6−i6i6−i6i6i6−i6i2i2−i2−i2−i2−i2i2i20000000000000000000000000000000000
χ834-444-44-4-40000-200002-2-22-2220000000000−2i22i22i2−2i2000−232323−230−i6i6i6−i6i6−i6−i6i6i2i2−i2−i2−i2−i2i2i20000000000000000000000000000000000
χ844-444-44-4-40000-200002-2-22-22200000000002i2−2i2−2i22i200023−23−23230−i6i6i6−i6i6−i6−i6i6−i2−i2i2i2i2i2−i2−i20000000000000000000000000000000000
χ854-444-44-4-40000-200002-2-22-22200000000002i2−2i2−2i22i2000−232323−230i6−i6−i6i6−i6i6i6−i6−i2−i2i2i2i2i2−i2−i20000000000000000000000000000000000
χ864-44-44-44-400004-444-4-44-44-44-400000000000000-44-40000400000000000000000000000000000000000000000000000000
χ874-44-44-44-40000-24-4-442-22-22-220000004i4i−4i−4i0000-22-200002−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000
χ884-44-44-44-40000-24-4-442-22-22-22000000−4i−4i4i4i0000-22-2000022i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000
χ894-44-44-44-40000-2-444-42-22-22-22000000000000002-220000-200000000−2i32i3−2i32i32i3−2i32i3−2i30000000000000000000000000000000000
χ904-44-44-44-40000-2-444-42-22-22-22000000000000002-220000-2000000002i3−2i32i3−2i3−2i32i3−2i32i30000000000000000000000000000000000
χ914-4-444-4-4444-4-4-200002222-2-2-200-2-22222−2222−2222−2222−2200000000−2−222−2−222−2−222−2−2220000000000000000000000000000000000
χ924-4-444-4-4444-4-4-200002222-2-2-200-2-222−2222−2222−2222−22220000000022−2−222−2−222−2−222−2−20000000000000000000000000000000000
χ934-4-444-4-44-4-444-200002222-2-2-20022-2-222−2222−22−2222−222200000000−2−222−2−22222−2−222−2−20000000000000000000000000000000000
χ944-4-444-4-44-4-444-200002222-2-2-20022-2-2−2222−222222−2222−220000000022−2−222−2−2−2−222−2−2220000000000000000000000000000000000
χ954-4-4-4-44444-44-4-244-4-422-2-222-24-4-22-2200000000-222-2-222-200000000000000000000000000000000000000000000000000
χ964-4-4-4-4444-44-44-244-4-422-2-222-2-442-22-200000000-22222-2-2-200000000000000000000000000000000000000000000000000

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