Finite Group Databasebeta

← Group #10742709

Character table — Group #10742709

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111111111111122222222222222224444444488888888888888888888888888888888888888121212121212121212121212121212122424242424242424
order122222222222222236666666666666662222444444444444446666121212121212121212121212121212121212121212121212222244444444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ5111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ6111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111-1-1-1-1-1-1
χ911111111111111111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1
χ1011111111111111111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111
χ1111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-1
χ1211111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-111
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ172222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ182222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000000000000
χ192222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000000000000000
χ202222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-1000000000000000000000000
χ212222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-222-2-222-2-21111-1-1-1-11111-1-1-1-11111-1-1-1-11111000000000000000000000000
χ222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-222-2-2221111-1-1-1-111111111-1-1-1-11111-1-1-1-1000000000000000000000000
χ232222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-22211111111-1-1-1-1-1-1-1-111111111-1-1-1-1000000000000000000000000
χ242222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-22222-2-211111111-1-1-1-11111-1-1-1-1-1-1-1-11111000000000000000000000000
χ25222-2-2-2-22222-22-2-2-22222-2-2-2-2-2-22222-2-200000000000000002-200000000000000000000000022-2-200002i2i−2i−2i00002i2i−2i−2i00000000
χ26222-2-2-2-22222-22-2-2-22222-2-2-2-2-2-22222-2-200000000000000002-200000000000000000000000022-2-20000−2i−2i2i2i0000−2i−2i2i2i00000000
χ27222-2-2-2-22222-22-2-2-22222-2-2-2-2-2-22222-2-20000000000000000-22000000000000000000000000-2-22200002i2i−2i−2i0000−2i−2i2i2i00000000
χ28222-2-2-2-22222-22-2-2-22222-2-2-2-2-2-22222-2-20000000000000000-22000000000000000000000000-2-2220000−2i−2i2i2i00002i2i−2i−2i00000000
χ2922-22-2-2-222-2-22-22-2222-2-222-2-2-2-222-2-22200000000002-200000000000000000022-2-200000000000022-2-2000022-2-2000000000000
χ3022-22-2-2-222-2-22-22-2222-2-222-2-2-2-222-2-22200000000002-200000000000000000022-2-2000000000000-2-2220000-2-222000000000000
χ3122-22-2-2-222-2-22-22-2222-2-222-2-2-2-222-2-2220000000000-22000000000000000000-2-22200000000000022-2-20000-2-222000000000000
χ3222-22-2-2-222-2-22-22-2222-2-222-2-2-2-222-2-2220000000000-22000000000000000000-2-222000000000000-2-222000022-2-2000000000000
χ3322-2-22-2-2-2-22-2-22222222-22-222-2-2-2-22-22-222-2-222-2-22-20000000022-2-222-2-222-2-20000000000000000000000000000000000000000
χ3422-2-22-2-2-2-22-2-22222222-22-222-2-2-2-22-22-222-2-2-2-222-220000000022-2-2-2-222-2-2220000000000000000000000000000000000000000
χ3522-2-22-2-2-2-22-2-22222222-22-222-2-2-2-22-22-2-2-22222-2-2-2200000000-2-22222-2-2-2-2220000000000000000000000000000000000000000
χ3622-2-22-2-2-2-22-2-22222222-22-222-2-2-2-22-22-2-2-222-2-2222-200000000-2-222-2-22222-2-20000000000000000000000000000000000000000
χ3722-2-22-2-2-2-22-2-22222-1-1-11-11-1-11111-11-1122-2-222-2-22-200000000-1-111-1-111-1-1113−33−333−3−333−3−33−33−3000000000000000000000000
χ3822-2-22-2-2-2-22-2-22222-1-1-11-11-1-11111-11-1122-2-222-2-22-200000000-1-111-1-111-1-111−33−33−3−333−3−333−33−33000000000000000000000000
χ3922-2-22-2-2-2-22-2-22222-1-1-11-11-1-11111-11-1122-2-2-2-222-2200000000-1-11111-1-111-1-13−33−333−3−3−3−333−33−33000000000000000000000000
χ4022-2-22-2-2-2-22-2-22222-1-1-11-11-1-11111-11-1122-2-2-2-222-2200000000-1-11111-1-111-1-1−33−33−3−33333−3−33−33−3000000000000000000000000
χ4122-2-22-2-2-2-22-2-22222-1-1-11-11-1-11111-11-11-2-22222-2-2-220000000011-1-1-1-11111-1-13−33−3−3−33333−3−3−33−33000000000000000000000000
χ4222-2-22-2-2-2-22-2-22222-1-1-11-11-1-11111-11-11-2-22222-2-2-220000000011-1-1-1-11111-1-1−33−3333−3−3−3−3333−33−3000000000000000000000000
χ4322-2-22-2-2-2-22-2-22222-1-1-11-11-1-11111-11-11-2-222-2-2222-20000000011-1-111-1-1-1-1113−33−3−3−333−3−3333−33−3000000000000000000000000
χ4422-2-22-2-2-2-22-2-22222-1-1-11-11-1-11111-11-11-2-222-2-2222-20000000011-1-111-1-1-1-111−33−3333−3−333−3−3−33−33000000000000000000000000
χ452-22-2-22-22-22-22-2-2222-2-22-2-22-22-22-22-2222-22-2000000000000002-22-20000000000000000000000002-22-20000000000000000002-2
χ462-22-2-22-22-22-22-2-2222-2-22-2-22-22-22-22-2222-22-2000000000000002-22-2000000000000000000000000-22-22000000000000000000-22
χ472-22-2-22-22-22-22-2-2222-2-22-2-22-22-22-22-222-22-2200000000000000-22-220000000000000000000000002-22-2000000000000000000-22
χ482-22-2-22-22-22-22-2-2222-2-22-2-22-22-22-22-222-22-2200000000000000-22-22000000000000000000000000-22-220000000000000000002-2
χ492-22-2-2-22-22-2-22222-22-2222-22-2-22-22-2-2-2200002i−2i2i−2i000000000000002i−2i2i−2i00000000000000000000000000002i−2i2i−2i0000002-20000
χ502-22-2-2-22-22-2-22222-22-2222-22-2-22-22-2-2-2200002i−2i2i−2i000000000000002i−2i2i−2i0000000000000000000000000000−2i2i−2i2i000000-220000
χ512-22-2-2-22-22-2-22222-22-2222-22-2-22-22-2-2-220000−2i2i−2i2i00000000000000−2i2i−2i2i00000000000000000000000000002i−2i2i−2i000000-220000
χ522-22-2-2-22-22-2-22222-22-2222-22-2-22-22-2-2-220000−2i2i−2i2i00000000000000−2i2i−2i2i0000000000000000000000000000−2i2i−2i2i0000002-20000
χ532-2-22-22-22-2-22-2222-22-22-2222-22-22-2-22-2-200002i−2i−2i2i000000000000002i−2i−2i2i000000000000000000000000000000002i−2i2i−2i00002-200
χ542-2-22-22-22-2-22-2222-22-22-2222-22-22-2-22-2-200002i−2i−2i2i000000000000002i−2i−2i2i00000000000000000000000000000000−2i2i−2i2i0000-2200
χ552-2-22-22-22-2-22-2222-22-22-2222-22-22-2-22-2-20000−2i2i2i−2i00000000000000−2i2i2i−2i000000000000000000000000000000002i−2i2i−2i0000-2200
χ562-2-22-22-22-2-22-2222-22-22-2222-22-22-2-22-2-20000−2i2i2i−2i00000000000000−2i2i2i−2i00000000000000000000000000000000−2i2i−2i2i00002-200
χ572-2-22-2-22-2222-2-2-2222-2-2-2-222-2-22-22222-22-2-22000000000000002-2-2200000000000000000000000000002-22-2000000002-2000000
χ582-2-22-2-22-2222-2-2-2222-2-2-2-222-2-22-22222-22-2-22000000000000002-2-220000000000000000000000000000-22-2200000000-22000000
χ592-2-22-2-22-2222-2-2-2222-2-2-2-222-2-22-22222-2-222-200000000000000-222-200000000000000000000000000002-22-200000000-22000000
χ602-2-22-2-22-2222-2-2-2222-2-2-2-222-2-22-22222-2-222-200000000000000-222-20000000000000000000000000000-22-22000000002-2000000
χ612-2-2-222-2-22222-22-2-22-2-2-22-2-222-2-2222-22000000000000002-200000000000000000000002-22-2000000002i−2i−2i2i2i−2i−2i2i000000000000
χ622-2-2-222-2-22222-22-2-22-2-2-22-2-222-2-2222-22000000000000002-200000000000000000000002-22-200000000−2i2i2i−2i−2i2i2i−2i000000000000
χ632-2-2-222-2-22222-22-2-22-2-2-22-2-222-2-2222-2200000000000000-220000000000000000000000-22-22000000002i−2i−2i2i−2i2i2i−2i000000000000
χ642-2-2-222-2-22222-22-2-22-2-2-22-2-222-2-2222-2200000000000000-220000000000000000000000-22-2200000000−2i2i2i−2i2i−2i−2i2i000000000000
χ652-2-2-22-222-2-2222-2-222-22-2-2-2-22-222-2-22220000000000002-2000000000000000000002-22-2000000002-2-22000000002-2-2200000000
χ662-2-2-22-222-2-2222-2-222-22-2-2-2-22-222-2-22220000000000002-2000000000000000000002-22-200000000-222-200000000-222-200000000
χ672-2-2-22-222-2-2222-2-222-22-2-2-2-22-222-2-2222000000000000-2200000000000000000000-22-22000000002-2-2200000000-222-200000000
χ682-2-2-22-222-2-2222-2-222-22-2-2-2-22-222-2-2222000000000000-2200000000000000000000-22-2200000000-222-2000000002-2-2200000000
χ6944444-4-4-4-4-444-4-44-444-44-4444-4-4-4-4-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ7044444-4-4-4-4-444-4-44-4-2-22-22-2-2-222222-22-20000000000000000000000000023−2323−230000000000000000000000000000000000000000
χ7144444-4-4-4-4-444-4-44-4-2-22-22-2-2-222222-22-200000000000000000000000000−2323−23230000000000000000000000000000000000000000
χ72444-4-444-4-4-44-4-44-4444-444-4-4-444-4-4-444-40000000000000000000000000000000000000000000000000000000000000000000000
χ73444-4-444-4-4-44-4-44-44-2-22-2-2222-2-2222-2-2200000000000000000000000000000023−23−2323000000000000000000000000000000000000
χ74444-4-444-4-4-44-4-44-44-2-22-2-2222-2-2222-2-22000000000000000000000000000000−232323−23000000000000000000000000000000000000
χ75444-4-4-4-44444-44-4-4-4-2-2-2-2222222-2-2-2-22200000000000000004-4000000000000000000000000-2-222000000000000000000000000
χ76444-4-4-4-44444-44-4-4-4-2-2-2-2222222-2-2-2-2220000000000000000-4400000000000000000000000022-2-2000000000000000000000000
χ7744-44-444-4-44-444-4-4-4444-4-44-4-444-4-44-4-440000000000000000000000000000000000000000000000000000000000000000000000
χ7844-44-444-4-44-444-4-4-4-2-2-222-222-2-222-222-200000000000000000000000000000000000000000023−23−2323000000000000000000000000
χ7944-44-444-4-44-444-4-4-4-2-2-222-222-2-222-222-2000000000000000000000000000000000000000000−232323−23000000000000000000000000
χ8044-44-4-4-444-4-44-44-44-2-222-2-22222-2-222-2-200000000004-4000000000000000000-2-222000000000000000000000000000000000000
χ8144-44-4-4-444-4-44-44-44-2-222-2-22222-2-222-2-20000000000-4400000000000000000022-2-2000000000000000000000000000000000000
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χ8344-4-444444-4-4-4-4-44-4-2-22222-2-2-2-2-2-222220000000000000000000000000023−23−23230000000000000000000000000000000000000000
χ8444-4-444444-4-4-4-4-44-4-2-22222-2-2-2-2-2-2222200000000000000000000000000−232323−230000000000000000000000000000000000000000
χ854-44444-4-44-4-4-44-4-444-444-44-444-4-44-4-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ864-44444-4-44-4-4-44-4-44-22-2-22-22-2-222-222-22000000000000000000000000000000000023−23−232300000000000000000000000000000000
χ874-44444-4-44-4-4-44-4-44-22-2-22-22-2-222-222-220000000000000000000000000000000000−232323−2300000000000000000000000000000000
χ884-4444-444-44-4-4-44-4-44-4-4444-44-444-44-4-4-40000000000000000000000000000000000000000000000000000000000000000000000
χ894-4444-444-44-4-4-44-4-4-222-2-2-22-22-2-22-22220000000000000000000000000000000000000023−23−23230000000000000000000000000000
χ904-4444-444-44-4-4-44-4-4-222-2-2-22-22-2-22-222200000000000000000000000000000000000000−232323−230000000000000000000000000000
χ914-44-4-44-44-44-44-4-444-222-222-22-22-22-22-2-24-44-400000000000000-22-22000000000000000000000000000000000000000000000000
χ924-44-4-44-44-44-44-4-444-222-222-22-22-22-22-2-2-44-44000000000000002-22-2000000000000000000000000000000000000000000000000
χ934-44-4-4-44-44-4-44444-4-22-2-2-22-222-22-2222-200004i−4i4i−4i00000000000000−2i2i−2i2i00000000000000000000000000000000000000000000
χ944-44-4-4-44-44-4-44444-4-22-2-2-22-222-22-2222-20000−4i4i−4i4i000000000000002i−2i2i−2i00000000000000000000000000000000000000000000
χ954-4-44-44-44-4-44-4444-4-22-22-2-2-22-22-222-22200004i−4i−4i4i00000000000000−2i2i2i−2i00000000000000000000000000000000000000000000
χ964-4-44-44-44-4-44-4444-4-22-22-2-2-22-22-222-2220000−4i4i4i−4i000000000000002i−2i−2i2i00000000000000000000000000000000000000000000
χ974-4-44-4-44-4444-4-4-444-22222-2-222-22-2-2-2-224-4-4400000000000000-222-2000000000000000000000000000000000000000000000000
χ984-4-44-4-44-4444-4-4-444-22222-2-222-22-2-2-2-22-444-4000000000000002-2-22000000000000000000000000000000000000000000000000
χ994-4-4-444-4-44444-44-4-4-2222-222-2-222-2-2-22-2000000000000004-40000000000000000000000-22-220000000000000000000000000000
χ1004-4-4-444-4-44444-44-4-4-2222-222-2-222-2-2-22-200000000000000-4400000000000000000000002-22-20000000000000000000000000000
χ1014-4-4-44-444-4-4444-4-44-22-22222-22-2-222-2-2-20000000000004-400000000000000000000-22-2200000000000000000000000000000000
χ1024-4-4-44-444-4-4444-4-44-22-22222-22-2-222-2-2-2000000000000-44000000000000000000002-22-200000000000000000000000000000000

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