Finite Group Databasebeta

← Group #72267891

Character table — Group #72267891

Order 6144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size11112244446666888888888812121212121212122424242424242424242424246464646464646464646464646464646496969696969696969696969696969696128128128128128128128128128128128128128128128128128128128128128128128128
order122222222222222222224444444444442222444444443366666666666666444444448888888866666666666666661212121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i321111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ311111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i321111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ41111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ51111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i3211111111-1-1-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32
χ61111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i3211111111-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32
χ7111111-1-1-1-11111-1-111-1-111-1-11111111111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1
χ8111111-1-1-1-11111-1-111-1-111-1-11111111111-1-1-1-1-1-111-1-1−1−i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1+i321111-1-1-1-11111-1-1-1-1−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ9111111-1-1-1-11111-1-111-1-111-1-11111111111-1-1-1-1-1-111-1-1−1+i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1−i321111-1-1-1-11111-1-1-1-1−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ10111111-1-1-1-11111-1-1-1-111-1-11111111111-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-111
χ11111111-1-1-1-11111-1-1-1-111-1-11111111111-1-111-1-1-1-1-1-111−1−i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1+i321111-1-1-1-1-1-1-1-11111−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ12111111-1-1-1-11111-1-1-1-111-1-11111111111-1-111-1-1-1-1-1-111−1+i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1−i321111-1-1-1-1-1-1-1-11111−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ132-2-222-222-2-222-2-22-22-22-22-22-22222-2-2-2-22-22-222-2-22-22-2-1-11111-1-11111-1-1-1-100000000000000001-11-11-11-11-11-11-11-11-11-11-11-1
χ142-2-222-222-2-222-2-22-22-22-22-22-22222-2-2-2-22-22-222-2-22-22-21+i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321+i321−i320000000000000000−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32
χ152-2-222-222-2-222-2-22-22-22-22-22-22222-2-2-2-22-22-222-2-22-22-21−i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321−i321+i320000000000000000−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32
χ162-2-222-222-2-222-2-22-2-22-22-22-222222-2-2-2-2-22-2222-2-2-22-22-1-11111-1-11111-1-1-1-100000000000000001-11-1-11-111-11-1-11-11-11-11-11-11
χ172-2-222-222-2-222-2-22-2-22-22-22-222222-2-2-2-2-22-2222-2-2-22-221+i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321+i321−i320000000000000000−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32
χ182-2-222-222-2-222-2-22-2-22-22-22-222222-2-2-2-2-22-2222-2-2-22-221−i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321−i321+i320000000000000000−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32
χ192-2-222-2-2-22222-2-2-222-2-222-2-222222-2-2-2-22-2-22-2-2222-2-22-1-111-1-11111-1-111-1-100000000000000001-1-111-1-111-1-111-1-111-1-111-1-11
χ202-2-222-2-2-22222-2-2-222-2-222-2-222222-2-2-2-22-2-22-2-2222-2-221+i321−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1+i32−1+i321+i321−i320000000000000000−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32
χ212-2-222-2-2-22222-2-2-222-2-222-2-222222-2-2-2-22-2-22-2-2222-2-221−i321+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1−i32−1−i321−i321+i320000000000000000−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32
χ222-2-222-2-2-22222-2-2-22-222-2-222-22222-2-2-2-2-222-2-2-222-222-2-1-111-1-11111-1-111-1-100000000000000001-1-11-111-11-1-11-111-1-111-1-111-1
χ232-2-222-2-2-22222-2-2-22-222-2-222-22222-2-2-2-2-222-2-2-222-222-21+i321−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1+i32−1+i321+i321−i320000000000000000−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i32
χ242-2-222-2-2-22222-2-2-22-222-2-222-22222-2-2-2-2-222-2-2-222-222-21−i321+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1−i32−1−i321−i321+i320000000000000000−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i32
χ25333333333333333333333333333333333333333333330000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ263333333333333333-3-3-3-3-3-3-3-333333333-3-3-3-33333-3-3-3-30000000000000000-1-1-1-1-1-1-1-111111111000000000000000000000000
χ27333333-3-3-3-33333-3-333-3-333-3-33333333333-3-3-3-3-3-333-3-30000000000000000-1-1-1-11111-1-1-1-11111000000000000000000000000
χ28333333-3-3-3-33333-3-3-3-333-3-33333333333-3-333-3-3-3-3-3-3330000000000000000-1-1-1-111111111-1-1-1-1000000000000000000000000
χ294444-4-444444-44-4-4-42222-2-2-2-20000000022220000-2-2-2-211111111111111110000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ304444-4-444444-44-4-4-42222-2-2-2-20000000022220000-2-2-2-2−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i3200000000000000001+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ314444-4-444444-44-4-4-42222-2-2-2-20000000022220000-2-2-2-2−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i3200000000000000001−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ324444-4-444444-44-4-4-4-2-2-2-2222200000000-2-2-2-20000222211111111111111110000000000000000-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ334444-4-444444-44-4-4-4-2-2-2-2222200000000-2-2-2-200002222−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i3200000000000000001+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32
χ344444-4-444444-44-4-4-4-2-2-2-2222200000000-2-2-2-200002222−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i3200000000000000001−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32
χ354444-4-4-4-4-4-44-44-44422-2-2-2-2220000000022-2-20000-2-2221111-1-1-1-111-1-1-1-1110000000000000000-1-111-1-111-1-111-1-11111-1-111-1-1
χ364444-4-4-4-4-4-44-44-44422-2-2-2-2220000000022-2-20000-2-222−1−i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1+i3200000000000000001+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ374444-4-4-4-4-4-44-44-44422-2-2-2-2220000000022-2-20000-2-222−1+i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1−i3200000000000000001−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ384444-4-4-4-4-4-44-44-444-2-22222-2-200000000-2-222000022-2-21111-1-1-1-111-1-1-1-1110000000000000000-1-11111-1-1-1-11111-1-1-1-111-1-111
χ394444-4-4-4-4-4-44-44-444-2-22222-2-200000000-2-222000022-2-2−1−i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1+i3200000000000000001+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ404444-4-4-4-4-4-44-44-444-2-22222-2-200000000-2-222000022-2-2−1+i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1−i3200000000000000001−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ414-4-44-4444-4-44-4-44-442-22-2-22-22000000002-22-20000-22-2211-1-1-1-111-1-1-1-1111100000000000000001-11-11-11-11-11-11-11-1-11-11-11-11
χ424-4-44-4444-4-44-4-44-442-22-2-22-22000000002-22-20000-22-22−1−i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1+i320000000000000000−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32
χ434-4-44-4444-4-44-4-44-442-22-2-22-22000000002-22-20000-22-22−1+i32−1−i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1−i320000000000000000−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32
χ444-4-44-4444-4-44-4-44-44-22-222-22-200000000-22-2200002-22-211-1-1-1-111-1-1-1-1111100000000000000001-11-1-11-111-11-1-11-111-11-11-11-1
χ454-4-44-4444-4-44-4-44-44-22-222-22-200000000-22-2200002-22-2−1−i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1+i320000000000000000−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32
χ464-4-44-4444-4-44-4-44-44-22-222-22-200000000-22-2200002-22-2−1+i32−1−i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1−i320000000000000000−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32
χ474-4-44-44-4-4444-4-444-42-2-22-222-2000000002-2-220000-222-211-1-111-1-1-1-111-1-11100000000000000001-1-111-1-111-1-111-1-11-111-1-111-1
χ484-4-44-44-4-4444-4-444-42-2-22-222-2000000002-2-220000-222-2−1−i32−1+i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1+i320000000000000000−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i32
χ494-4-44-44-4-4444-4-444-42-2-22-222-2000000002-2-220000-222-2−1+i32−1−i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1−i320000000000000000−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i32
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χ10016-1616-1600-888-800000000000000000000000000000000001−i31+i31−i3−1+i3−1+i31−i31−i3−1+i31+i3−1−i3−1−i31+i31+i3−1−i3−1+i3−1−i30000000000000000000000000000000000000000

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