Finite Group Databasebeta

← Group #13178771

Character table — Group #13178771

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size112222222222222224444444444444444444444444444444444444444888888888888888888888888888888181818181818363636363636363636363636363636363636363636363636363636363636363636
order12222333444466612123333366666666666666121212121212121212121212121212121212121212666666666666666121212121212121212121212121212882424242422224444666666668881212121212121212242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111111
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1111-11-1-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11-111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ5111-1-11111-1-1111111111111-1-11-1-11-1-1111111-1-111-1-111-1-1111111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-11111-1-11-1-1-1-11111-1-111-1-1-1-1
χ6111-1-11111-1-1111111111111-1-11-1-11-1-1111111-1-111-1-111-1-1111111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1111-1-1-1-1111-1-111-1-1-1-11111-1-1-1-1
χ7111-1-11111-1-1111111111111-1-11-1-11-1-1111111-1-111-1-111-1-1111111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-11111111-1-1-111-1-1-1-1-1-111-1-11111
χ8111-1-11111-1-1111111111111-1-11-1-11-1-1111111-1-111-1-111-1-1111111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-1-111-111111111-1-1-1-11111
χ911-11-1111-11-111111111111-11-1-11-1-11-111111-11-11-11-11-11-11111111111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11111111-11-1-11-11-1-111-1-111-11-1-1-111-1-111-1-111-1-1
χ1011-11-1111-11-111111111111-11-1-11-1-11-111111-11-11-11-11-11-11111111111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1111111-11-111-11-111-1-111-1-1-11-111-1-111-1-1-1-111-1-1
χ1111-11-1111-11-111111111111-11-1-11-1-11-111111-11-11-11-11-11-11111111111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-11-111-1-11-11111-1-1111-11-1-1-1-111-1-111-1-111
χ1211-11-1111-11-111111111111-11-1-11-1-11-111111-11-11-11-11-11-11111111111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-1-1-111-1-11-111111-1-11111-1-111
χ1311-1-11111-1-1111111111111-1-11-1-11-1-1111111-1-111-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1111-1-11111-1-1-1-1-1-111111-1-1-1-1-1-1-1-111
χ1411-1-11111-1-1111111111111-1-11-1-11-1-1111111-1-111-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111111-111-1-1-111-1-1-1-11111-1-11-1-1-1-11111-1-1-1-111
χ1511-1-11111-1-1111111111111-1-11-1-11-1-1111111-1-111-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11-1-1-11-111-1-111-1-1-1-111-111-1-111111111-1-1
χ1611-1-11111-1-1111111111111-1-11-1-11-1-1111111-1-111-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1111-11-1-111-1-1111111-1-1-111-1-1-1-11111-1-1
χ172222222-122222-12222-1-1-1-1222222-1-1-12-1-1-1-1222-1-1-1-1222222-1-1-1-1-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-10000002220200000-1-1-1-1-1-1000-1-1000000000000
χ182222222-122222-12222-1-1-1-1222222-1-1-12-1-1-1-1222-1-1-1-1222222-1-1-1-1-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-1000000-2-2-20-20000011111100011000000000000
χ19222222-12222222-122-12-1-1-1222-1-1-1222-12-1-1-12222222-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-100000000020222-1-100000000000-1-1-1-1-1-1000000
χ20222222-12222222-122-12-1-1-1222-1-1-1222-12-1-1-12222222-1-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1000000000-20-2-2-21100000000000111111000000
χ2122222-1222222-122-1-1-1-12-1-1-1-1-1222222-1-12-1-1-1-1-122222222-1-1-1-122-1-1-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-122-1-1-1-1000000000000000022200000000-1-1-1-1-1-1
χ2222222-1222222-122-1-1-1-12-1-1-1-1-1222222-1-12-1-1-1-1-122222222-1-1-1-122-1-1-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-1-12-1-1-2-211110000000000000000-2-2-200000000111111
χ232222-2222-2-22-2222-2-22222222-222-222-222222-2-22-2-2-22-2-2-22-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222000000000000000000000000000000000000000
χ242222-222-1-2-22-22-12-2-22-1-1-1-122-222-2-1-112-1-1-1-1-2-22111-1-2-2-22-2-2111111112-1-1-1-12-1-1-1-1-21111-21111-211112-1-1-1-10000000000000000−i3i3−i3i3−i3i3000−i3i3000000000000
χ252222-222-1-2-22-22-12-2-22-1-1-1-122-222-2-1-112-1-1-1-1-2-22111-1-2-2-22-2-2111111112-1-1-1-12-1-1-1-1-21111-21111-211112-1-1-1-10000000000000000i3−i3i3−i3i3−i3000i3−i3000000000000
χ262222-22-12-2-22-222-1-2-2-12-1-1-122-2-1-1122-2-12-1-1-1-2-22-2-2-22111-111-2-2111111-12-1-1-1-12-1-1-11-21111-21111-2111-12-1-1-100000000000000−i3i300000000000−i3i3−i3i3−i3i3000000
χ272222-22-12-2-22-222-1-2-2-12-1-1-122-2-1-1122-2-12-1-1-1-2-22-2-2-22111-111-2-2111111-12-1-1-1-12-1-1-11-21111-21111-2111-12-1-1-100000000000000i3−i300000000000i3−i3i3−i3i3−i3000000
χ282222-2-122-2-22-2-12211-1-12-1-1-1-1122-222-2-1-12-1-111-1-2-2-22-2-2-221111-2-21111-1-12-1-1-1-12-1-111-21111-21111-211-1-12-1-10033−3−30000000000000000000000000003−33−33−3
χ292222-2-122-2-22-2-12211-1-12-1-1-1-1122-222-2-1-12-1-111-1-2-2-22-2-2-221111-2-21111-1-12-1-1-1-12-1-111-21111-21111-211-1-12-1-100−3−333000000000000000000000000000−33−33−33
χ30222-22222-22-2-2222-2-2222222-222-222-2222222-22-2-2-22-2-2-22-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-222222-2-2-2-2-222222-2-2-2-2-2000000000000000000000000000000000000000
χ31222-2222-1-22-2-22-12-2-22-1-1-1-12-222-22-11-12-1-1-1-1-22-211-11-2-22-2-2-2111111112-1-1-1-1-211112-1-1-1-1-211112-1-1-1-1-211110000000000000000−i3i3−i3i3i3−i3000i3−i3000000000000
χ32222-2222-1-22-2-22-12-2-22-1-1-1-12-222-22-11-12-1-1-1-1-22-211-11-2-22-2-2-2111111112-1-1-1-1-211112-1-1-1-1-211112-1-1-1-1-211110000000000000000i3−i3i3−i3−i3i3000−i3i3000000000000
χ33222-222-12-22-2-222-1-2-2-12-1-1-12-22-11-12-22-12-1-1-1-22-2-2-22-211-1111-2-2111111-12-1-1-11-2111-12-1-1-11-2111-12-1-1-11-211100000000000000−i3i300000000000i3−i3i3−i3−i3i3000000
χ34222-222-12-22-2-222-1-2-2-12-1-1-12-22-11-12-22-12-1-1-1-22-2-2-22-211-1111-2-2111111-12-1-1-11-2111-12-1-1-11-2111-12-1-1-11-211100000000000000i3−i300000000000−i3i3−i3i3i3−i3000000
χ35222-22-122-22-2-2-12211-1-12-1-1-11-12-222-22-1-12-1-11-11-2-22-2-2-22-21111-2-21111-1-12-1-111-211-1-12-1-111-211-1-12-1-111-2110033−3−30000000000000000000000000003−3−33−33
χ36222-22-122-22-2-2-12211-1-12-1-1-11-12-222-22-1-12-1-11-11-2-22-2-2-22-21111-2-21111-1-12-1-111-211-1-12-1-111-211-1-12-1-111-21100−3−333000000000000000000000000000−333−33−3
χ37222-2-222-12-2-222-12222-1-1-1-12-2-22-2-2-1112-1-1-1-12-2-2-1-11122-2-222-1-1-1-1-1-1-1-12-1-1-1-1-21111-211112-1-1-1-1-21111-2111100000022-20-200000-1-1-1-11100011000000000000
χ38222-2-222-12-2-222-12222-1-1-1-12-2-22-2-2-1112-1-1-1-12-2-2-1-11122-2-222-1-1-1-1-1-1-1-12-1-1-1-1-21111-211112-1-1-1-1-21111-21111000000-2-2202000001111-1-1000-1-1000000000000
χ39222-2-22-122-2-2222-122-12-1-1-12-2-2-1112-2-2-12-1-1-12-2-222-2-2-1-111-1-122-1-1-1-1-1-1-12-1-1-11-21111-2111-12-1-1-11-21111-211100000000020-2-22-1-1000000000001111-1-1000000
χ40222-2-22-122-2-2222-122-12-1-1-12-2-2-1112-2-2-12-1-1-12-2-222-2-2-1-111-1-122-1-1-1-1-1-1-12-1-1-11-21111-2111-12-1-1-11-21111-2111000000000-2022-21100000000000-1-1-1-111000000
χ41222-2-2-1222-2-22-122-1-1-1-12-1-1-1112-2-22-2-2-1-12-1-1-11122-2-222-2-2-1-1-1-122-1-1-1-1-1-12-1-111-21111-211-1-12-1-111-21111-21122-1-1-1-100000000000000002-2-200000000-1-11111
χ42222-2-2-1222-2-22-122-1-1-1-12-1-1-1112-2-22-2-2-1-12-1-1-11122-2-222-2-2-1-1-1-122-1-1-1-1-1-12-1-111-21111-211-1-12-1-111-21111-211-2-211110000000000000000-2220000000011-1-1-1-1
χ4322-2222222-2-2-2222-2-222222-222-222-222222222-2-2-22-2-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000
χ4422-22222-12-2-2-22-12-2-22-1-1-1-1-222-2221-1-12-1-1-1-12-2-21-111-22-2-2-2-211111111-211112-1-1-1-12-1-1-1-12-1-1-1-1-21111-211110000000000000000−i3i3i3−i3−i3i3000i3−i3000000000000
χ4522-22222-12-2-2-22-12-2-22-1-1-1-1-222-2221-1-12-1-1-1-12-2-21-111-22-2-2-2-211111111-211112-1-1-1-12-1-1-1-12-1-1-1-1-21111-211110000000000000000i3−i3−i3i3i3−i3000−i3i3000000000000
χ4622-2222-122-2-2-222-1-2-2-12-1-1-1-2221-1-1-222-12-1-1-12-2-2-22-2-21-11111-2-21111111-2111-12-1-1-1-12-1-1-1-12-1-1-11-21111-211100000000000000−i3i300000000000i3−i3−i3i3i3−i3000000
χ4722-2222-122-2-2-222-1-2-2-12-1-1-1-2221-1-1-222-12-1-1-12-2-2-22-2-21-11111-2-21111111-2111-12-1-1-1-12-1-1-1-12-1-1-11-21111-211100000000000000i3−i300000000000−i3i3i3−i3−i3i3000000
χ4822-222-1222-2-2-2-12211-1-12-1-11-1-1-222-222-1-12-1-1-111-22-2-2-22-2-21111-2-2111111-211-1-12-1-1-1-12-1-1-1-12-1-111-21111-2110033−3−3000000000000000000000000000−333−3−33
χ4922-222-1222-2-2-2-12211-1-12-1-11-1-1-222-222-1-12-1-1-111-22-2-2-22-2-21111-2-2111111-211-1-12-1-1-1-12-1-1-1-12-1-111-21111-21100−3−3330000000000000000000000000003−3−333−3
χ5022-22-222-1-22-222-12222-1-1-1-1-22-2-22-21-112-1-1-1-1-22-2-11-112-22-222-1-1-1-1-1-1-1-1-211112-1-1-1-1-21111-211112-1-1-1-1-211110000002-220-200000-1-111-1-100011000000000000
χ5122-22-222-1-22-222-12222-1-1-1-1-22-2-22-21-112-1-1-1-1-22-2-11-112-22-222-1-1-1-1-1-1-1-1-211112-1-1-1-1-21111-211112-1-1-1-1-21111000000-22-2020000011-1-111000-1-1000000000000
χ5222-22-22-12-22-2222-122-12-1-1-1-22-21-11-22-2-12-1-1-1-22-22-22-2-11-11-1-122-1-1-1-1-1-11-2111-12-1-1-11-21111-2111-12-1-1-11-211100000000020-22-2-1-10000000000011-1-111000000
χ5322-22-22-12-22-2222-122-12-1-1-1-22-21-11-22-2-12-1-1-1-22-22-22-2-11-11-1-122-1-1-1-1-1-11-2111-12-1-1-11-21111-2111-12-1-1-11-2111000000000-202-221100000000000-1-111-1-1000000
χ5422-22-2-122-22-22-122-1-1-1-12-1-11-11-22-2-22-2-1-12-1-11-112-22-22-22-2-1-1-1-122-1-1-1-111-211-1-12-1-111-21111-211-1-12-1-111-21122-1-1-1-10000000000000000-22-20000000011-1-111
χ5522-22-2-122-22-22-122-1-1-1-12-1-11-11-22-2-22-2-1-12-1-11-112-22-22-22-2-1-1-1-122-1-1-1-111-211-1-12-1-111-21111-211-1-12-1-111-211-2-2111100000000000000002-2200000000-1-111-1-1
χ5622-2-2222-1-2-2222-12222-1-1-1-1-2-22-2-2211-12-1-1-1-1-2-22-111-12-2-2222-1-1-1-1-1-1-1-1-21111-211112-1-1-1-1-21111-211112-1-1-1-10000002-2-20200000-1-11111000-1-1000000000000
χ5722-2-2222-1-2-2222-12222-1-1-1-1-2-22-2-2211-12-1-1-1-1-2-22-111-12-2-2222-1-1-1-1-1-1-1-1-21111-211112-1-1-1-1-21111-211112-1-1-1-1000000-2220-20000011-1-1-1-100011000000000000
χ5822-2-222-12-2-22222-122-12-1-1-1-2-2211-1-2-22-12-1-1-1-2-222-2-22-111-1-1-122-1-1-1-1-1-11-21111-2111-12-1-1-11-21111-2111-12-1-1-1000000000202-2-2-1-100000000000-1-11111000000
χ5922-2-222-12-2-22222-122-12-1-1-1-2-2211-1-2-22-12-1-1-1-2-222-2-22-111-1-1-122-1-1-1-1-1-11-21111-2111-12-1-1-11-21111-2111-12-1-1-1000000000-20-222110000000000011-1-1-1-1000000
χ6022-2-22-122-2-222-122-1-1-1-12-1-111-1-2-22-2-22-1-12-1-111-12-2-222-2-22-1-1-1-122-1-1-1-111-21111-211-1-12-1-111-21111-211-1-12-1-122-1-1-1-10000000000000000-2-22000000001111-1-1
χ6122-2-22-122-2-222-122-1-1-1-12-1-111-1-2-22-2-22-1-12-1-111-12-2-222-2-22-1-1-1-122-1-1-1-111-21111-211-1-12-1-111-21111-211-1-12-1-1-2-21111000000000000000022-200000000-1-1-1-111
χ6222-2-2-2222222-2222-2-222222-2-2-2-2-2-2-2-2-222222222-2222-2222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222222000000000000000000000000000000000000000
χ6322-2-2-222-1222-22-12-2-22-1-1-1-1-2-2-2-2-2-21112-1-1-1-12221-1-1-1-2222-2-211111111-21111-21111-211112-1-1-1-12-1-1-1-12-1-1-1-10000000000000000−i3i3i3−i3i3−i3000−i3i3000000000000
χ6422-2-2-222-1222-22-12-2-22-1-1-1-1-2-2-2-2-2-21112-1-1-1-12221-1-1-1-2222-2-211111111-21111-21111-211112-1-1-1-12-1-1-1-12-1-1-1-10000000000000000i3−i3−i3i3−i3i3000i3−i3000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.