Finite Group Databasebeta

← Group #10751708

Character table — Group #10751708

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111111111112222222222222222444488888888888888888888888888888888888888881212121212121212242424242424242424242424
order1222222222222222366666666666666644444444444444441212121212121212121212121212121212121212121212121212121244444444224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ5111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111111111111111111111111111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111111111111111111111111111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ1111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111
χ1211111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1
χ1311111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111
χ1411111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1
χ1511111111111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ1611111111111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ172222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ182222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-11111111100000000000000000000
χ192222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000000000
χ202222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ212222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-222-2-222-2-2-1-1-1-11111-1-1-1-111111111-1-1-1-1111100000000000000000000
χ222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-222-2-222-1-1-1-111111111-1-1-1-111111111-1-1-1-100000000000000000000
χ232222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-22222-2-2-2-2221111-1-1-1-1-1-1-1-1111111111111-1-1-1-100000000000000000000
χ242222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222-2-22222-2-21111-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000000000000000
χ25222222-22-2-2-22-2-2-2-22222222-2-2-2-22-2-2-2-200002-2000000000022-2-200000000000000000000000022-2-200002-20000000000
χ26222222-22-2-2-22-2-2-2-22222222-2-2-2-22-2-2-2-200002-2000000000022-2-2000000000000000000000000-2-2220000-220000000000
χ27222222-22-2-2-22-2-2-2-22222222-2-2-2-22-2-2-2-20000-220000000000-2-22200000000000000000000000022-2-20000-220000000000
χ28222222-22-2-2-22-2-2-2-22222222-2-2-2-22-2-2-2-20000-220000000000-2-222000000000000000000000000-2-22200002-20000000000
χ29222-2-2-2-2222-2-22-22-2222-2-2-2-222-2-2222-2-200000000002i−2i00000000000000002i2i−2i−2i000000000000000022-2-2002i−2i00000000
χ30222-2-2-2-2222-2-22-22-2222-2-2-2-222-2-2222-2-200000000002i−2i00000000000000002i2i−2i−2i0000000000000000-2-22200−2i2i00000000
χ31222-2-2-2-2222-2-22-22-2222-2-2-2-222-2-2222-2-20000000000−2i2i0000000000000000−2i−2i2i2i000000000000000022-2-200−2i2i00000000
χ32222-2-2-2-2222-2-22-22-2222-2-2-2-222-2-2222-2-20000000000−2i2i0000000000000000−2i−2i2i2i0000000000000000-2-222002i−2i00000000
χ3322-22-2-2-2-22-222-2-22222-222-2-22-2-2-2-22-22222-2-2000000000000000000000000000022-2-20000000000000000000000002-22-2
χ3422-22-2-2-2-22-222-2-22222-222-2-22-2-2-2-22-22222-2-2000000000000000000000000000022-2-2000000000000000000000000-22-22
χ3522-22-2-2-2-22-222-2-22222-222-2-22-2-2-2-22-222-2-2220000000000000000000000000000-2-2220000000000000000000000002-2-22
χ3622-22-2-2-2-22-222-2-22222-222-2-22-2-2-2-22-222-2-2220000000000000000000000000000-2-222000000000000000000000000-222-2
χ372-22-22-2-2-2-2-2-2222222-222-22-2222-2-2-2-2-222-22-2000000002-22-200000000000000002-22-222-2-222-2-200000000000000000000
χ382-22-22-2-2-2-2-2-2222222-222-22-2222-2-2-2-2-222-22-200000000-22-2200000000000000002-22-2-2-222-2-22200000000000000000000
χ392-22-22-2-2-2-2-2-2222222-222-22-2222-2-2-2-2-22-22-22000000002-2-220000000000000000-22-2222-2-2-2-22200000000000000000000
χ402-22-22-2-2-2-2-2-2222222-222-22-2222-2-2-2-2-22-22-2200000000-222-20000000000000000-22-22-2-22222-2-200000000000000000000
χ412-22-22-2-2-2-2-2-222222-11-1-11-11-1-1-111111-12-22-2000000002-22-23−33−333−3−333−3−33−33−3-11-11-1-111-1-11100000000000000000000
χ422-22-22-2-2-2-2-2-222222-11-1-11-11-1-1-111111-12-22-2000000002-22-2−33−33−3−333−3−333−33−33-11-11-1-111-1-11100000000000000000000
χ432-22-22-2-2-2-2-2-222222-11-1-11-11-1-1-111111-12-22-200000000-22-223−33−333−3−3−3−333−33−33-11-1111-1-111-1-100000000000000000000
χ442-22-22-2-2-2-2-2-222222-11-1-11-11-1-1-111111-12-22-200000000-22-22−33−33−3−33333−3−33−33−3-11-1111-1-111-1-100000000000000000000
χ452-22-22-2-2-2-2-2-222222-11-1-11-11-1-1-111111-1-22-22000000002-2-223−33−3−3−33333−3−3−33−331-11-1-1-11111-1-100000000000000000000
χ462-22-22-2-2-2-2-2-222222-11-1-11-11-1-1-111111-1-22-22000000002-2-22−33−3333−3−3−3−3333−33−31-11-1-1-11111-1-100000000000000000000
χ472-22-22-2-2-2-2-2-222222-11-1-11-11-1-1-111111-1-22-2200000000-222-23−33−3−3−333−3−3333−33−31-11-111-1-1-1-11100000000000000000000
χ482-22-22-2-2-2-2-2-222222-11-1-11-11-1-1-111111-1-22-2200000000-222-2−33−3333−3−333−3−3−33−331-11-111-1-1-1-11100000000000000000000
χ492-2-222-2-22-222-2-222-22-2-2-222-22-22-22-222-2000000002i−2i000000000000002i−2i2i−2i000000000000000000002-22-200002i−2i000000
χ502-2-222-2-22-222-2-222-22-2-2-222-22-22-22-222-2000000002i−2i000000000000002i−2i2i−2i00000000000000000000-22-220000−2i2i000000
χ512-2-222-2-22-222-2-222-22-2-2-222-22-22-22-222-200000000−2i2i00000000000000−2i2i−2i2i000000000000000000002-22-20000−2i2i000000
χ522-2-222-2-22-222-2-222-22-2-2-222-22-22-22-222-200000000−2i2i00000000000000−2i2i−2i2i00000000000000000000-22-2200002i−2i000000
χ532-2-2-2-2222-22-22-2-2222-2-22-2-222-2-222-22-222-2-2200000000000000000000000000002-2-22000000002-22-22-2-22000000000000
χ542-2-2-2-2222-22-22-2-2222-2-22-2-222-2-222-22-222-2-2200000000000000000000000000002-2-2200000000-22-22-222-2000000000000
χ552-2-2-2-2222-22-22-2-2222-2-22-2-222-2-222-22-22-222-20000000000000000000000000000-222-2000000002-22-2-222-2000000000000
χ562-2-2-2-2222-22-22-2-2222-2-22-2-222-2-222-22-22-222-20000000000000000000000000000-222-200000000-22-222-2-22000000000000
χ572-2-2-2-22-222-22222-2-22-2-22-2-22-222-222-22-20000002i−2i0000000000002i−2i2i−2i000000000000000000002-2-2200000000002i−2i0000
χ582-2-2-2-22-222-22222-2-22-2-22-2-22-222-222-22-20000002i−2i0000000000002i−2i2i−2i00000000000000000000-222-20000000000−2i2i0000
χ592-2-2-2-22-222-22222-2-22-2-22-2-22-222-222-22-2000000−2i2i000000000000−2i2i−2i2i000000000000000000002-2-220000000000−2i2i0000
χ602-2-2-2-22-222-22222-2-22-2-22-2-22-222-222-22-2000000−2i2i000000000000−2i2i−2i2i00000000000000000000-222-200000000002i−2i0000
χ61444444-44-4-4-44-4-4-4-4-2-2-2-2-2-2-22222-2222200004-40000000000-2-22200000000000000000000000000000000000000000000
χ62444444-44-4-4-44-4-4-4-4-2-2-2-2-2-2-22222-222220000-44000000000022-2-200000000000000000000000000000000000000000000
χ63444-4-4-444-4-44-4-44-44444-4-4-4-4-4-4444-4-4440000000000000000000000000000000000000000000000000000000000000000
χ64444-4-4-444-4-44-4-44-44-2-2-2222222-2-2-222-2-20000000000000000000000000000000000000000−2i32i3−2i32i300000000000000000000
χ65444-4-4-444-4-44-4-44-44-2-2-2222222-2-2-222-2-200000000000000000000000000000000000000002i3−2i32i3−2i300000000000000000000
χ66444-4-4-4-4444-4-44-44-4-2-2-22222-2-222-2-2-22200000000004i−4i0000000000000000−2i−2i2i2i00000000000000000000000000000000
χ67444-4-4-4-4444-4-44-44-4-2-2-22222-2-222-2-2-2220000000000−4i4i00000000000000002i2i−2i−2i00000000000000000000000000000000
χ6844-44-4-44-4-44-4444-4-444-444-4-4-4444-4-44-4-40000000000000000000000000000000000000000000000000000000000000000
χ6944-44-4-44-4-44-4444-4-4-2-22-2-2222-2-2-222-22200000000000000000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ7044-44-4-44-4-44-4444-4-4-2-22-2-2222-2-2-222-222000000000000000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ7144-44-4-4-4-44-444-4-444-2-22-2-222-22222-22-2-244-4-40000000000000000000000000000-2-2220000000000000000000000000000
χ7244-44-4-4-4-44-444-4-444-2-22-2-222-22222-22-2-2-4-444000000000000000000000000000022-2-20000000000000000000000000000
χ7344-4-4444-44-4-4-4-444-444-4-4-4444-444-44-4-4-40000000000000000000000000000000000000000000000000000000000000000
χ7444-4-4444-44-4-4-4-444-4-2-2222-2-2-22-2-22-2222000000000000000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ7544-4-4444-44-4-4-4-444-4-2-2222-2-2-22-2-22-22220000000000000000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ7644-4-444-4-4-444-44-4-4444-4-4-444-44-4-4-4-44440000000000000000000000000000000000000000000000000000000000000000
χ7744-4-444-4-4-444-44-4-44-2-2222-2-22-22222-2-2-2000000000000000000000000000000000000−2i32i3−2i32i3000000000000000000000000
χ7844-4-444-4-4-444-44-4-44-2-2222-2-22-22222-2-2-20000000000000000000000000000000000002i3−2i32i3−2i3000000000000000000000000
χ794-444-444-4-4-44-44-44-44-44-44-4444-44-4-4-44-40000000000000000000000000000000000000000000000000000000000000000
χ804-444-444-4-4-44-44-44-4-22-22-22-2-2-22-2222-220000000000000000000000000000−2i32i32i3−2i300000000000000000000000000000000
χ814-444-444-4-4-44-44-44-4-22-22-22-2-2-22-2222-2200000000000000000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ824-444-44-4-444-4-4-44-444-44-44-44-4-44-4-444-440000000000000000000000000000000000000000000000000000000000000000
χ834-444-44-4-444-4-4-44-44-22-22-22-222-222-2-22-20000000000000000000000000000000000000000−2i32i32i3−2i300000000000000000000
χ844-444-44-4-444-4-4-44-44-22-22-22-222-222-2-22-200000000000000000000000000000000000000002i3−2i3−2i32i300000000000000000000
χ854-44-44-44-44444-4-4-4-44-444-44-4-4-4-44-4444-40000000000000000000000000000000000000000000000000000000000000000
χ864-44-44-44-44444-4-4-4-4-22-2-22-22222-22-2-2-22000000000000000023−23−232300000000000000000000000000000000000000000000
χ874-44-44-44-44444-4-4-4-4-22-2-22-22222-22-2-2-220000000000000000−232323−2300000000000000000000000000000000000000000000
χ884-4-444-4444-4-4-44-4-444-4-4-444-4-44-4444-4-440000000000000000000000000000000000000000000000000000000000000000
χ894-4-444-4444-4-4-44-4-44-2222-2-222-22-2-2-222-2000000000000000000000000000000000000−2i32i32i3−2i3000000000000000000000000
χ904-4-444-4444-4-4-44-4-44-2222-2-222-22-2-2-222-20000000000000000000000000000000000002i3−2i3−2i32i3000000000000000000000000
χ914-4-444-4-44-444-4-444-4-2222-2-22-22-22-22-2-22000000004i−4i00000000000000−2i2i−2i2i000000000000000000000000000000000000
χ924-4-444-4-44-444-4-444-4-2222-2-22-22-22-22-2-2200000000−4i4i000000000000002i−2i2i−2i000000000000000000000000000000000000
χ934-4-4-4-4444-44-44-4-444-222-222-2-222-2-22-22-24-4-440000000000000000000000000000-222-20000000000000000000000000000
χ944-4-4-4-4444-44-44-4-444-222-222-2-222-2-22-22-2-444-400000000000000000000000000002-2-220000000000000000000000000000
χ954-4-4-4-44-444-44444-4-4-222-222-22-2-22-2-22-220000004i−4i000000000000−2i2i−2i2i0000000000000000000000000000000000000000
χ964-4-4-4-44-444-44444-4-4-222-222-22-2-22-2-22-22000000−4i4i0000000000002i−2i2i−2i0000000000000000000000000000000000000000

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