Finite Group Databasebeta

← Group #13172358

Character table — Group #13172358

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222222444444444444444444888888888888881212121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363636363636108108
order1222223336666666663336666666666666663666666666666624444412121212121212122222666666661212121212121212121212121212121222446666661212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-111111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ511111111111111111111111111111111111111111111111111-11111-11111111111111111-1-1-1-1-11111-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111111
χ711111111111111111111111111111111111111111111111111-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-111-11-1-111-1-111-1-111-1-111111111-11-11-1-1-1-111-1-111-1-11-11-1-1-111-1-111-1-1-11
χ101111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-111-1-11-111-1-1-1-111-1-111-1-1-1-11111-11-1-11-1-1-111-1-1-1-1111-1-111111-1-1-1-1111-1
χ111111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-11-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-111-111-1-11111-1-11-1
χ121111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-11-11-11-1-1-111-1-11111-1-111111111-1-11-11-1-1-1-1-111-1-111-11-11-1-1-1-111-1-111-11
χ131111-1-1111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1-11-11-1111-1-111-1-111-1-11111-1-1-1-111-11-111111-1-111-1-1-11-11-1-1-1-111-1-1111-1
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χ1922222222-1222-1-1-12222-1-12222-1-12-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-22200-22222000000000000-21111-1-100-211-1-1-1-10000-2-200001111000000
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χ9888-8-800-48-4-8-444-448-84-4-42000000442-2-44-44-22000000-22-200000000000000000000000000000000000000000000000000000000000000
χ9988-8-800-4-484-44-88-8-4442-4-4000000-24-442-2-4442000000-22-200000000000000000000000000000000000000000000000000000000000000
χ10088-8-800-4-4-44-444-44-444222000000-2-22-22-22-2-2-10000001-11−3i33i3−3i33i30000000000000000000000000000000000000000000000000000000000
χ10188-8-800-4-4-44-444-44-444222000000-2-22-22-22-2-2-10000001-113i3−3i33i3−3i30000000000000000000000000000000000000000000000000000000000
χ1028-88-8008-4-44-8844-44-4-8-42-40000004-24-44-4-2242000000-2-2200000000000000000000000000000000000000000000000000000000000000
χ1038-88-800-48-4-84-444-4-884-4-4200000044-224-44-4-22000000-2-2200000000000000000000000000000000000000000000000000000000000000
χ1048-88-800-4-4844-4-8-884-442-4-4000000-244-4-224-442000000-2-2200000000000000000000000000000000000000000000000000000000000000
χ1058-88-800-4-4-444-444-44-44222000000-2-2-22-22-22-2-100000011-1−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000000
χ1068-88-800-4-4-444-444-44-44222000000-2-2-22-22-22-2-100000011-13i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000000
χ1078-8-888-8-4-4-4-444-44444-4222-44-44-4422-2-2-2-2-2-22-12-22-22-2-111-1-1110000000000000000000000000000000000000000000000000000000000
χ1088-8-88-88-4-4-4-444-44444-42224-44-44-422-2-2-2-2-2-22-1-22-22-22-11111-1-10000000000000000000000000000000000000000000000000000000000

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