Finite Group Databasebeta

← Group #13173179

Character table — Group #13173179

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size112222222224444444444444181836336666666661212121212121212121212121254541084488888888816161616161616161616161616727214444888888888161616161616161616161616167272144
order1233334666641212121212121212121212128842266664666641212121212121212121212128843633331266661212121212121212121212121224241236333312666612121212121212121212121212242412
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1111111111111111111111111-1-1-1111111111111111111111111-1-1-1111111111111111111111111-1-1-1
χ311111111111-11111-1-1-1-1-1-1-1-111-111111111111-11111-1-1-1-1-1-1-1-111-111111111111-11111-1-1-1-1-1-1-1-111-111111111111-11111-1-1-1-1-1-1-1-111-1
χ411111111111-11111-1-1-1-1-1-1-1-1-1-1111111111111-11111-1-1-1-1-1-1-1-1-1-1111111111111-11111-1-1-1-1-1-1-1-1-1-1111111111111-11111-1-1-1-1-1-1-1-1-1-11
χ5222222-222220-2-2-2-200000000000222222-222220-2-2-2-200000000000222222-222220-2-2-2-200000000000222222-222220-2-2-2-200000000000
χ6222-1-1-122-1-1-122-1-1-122-1-1-1-1-1-1000222-1-1-122-1-1-122-1-1-122-1-1-1-1-1-1000222-1-1-122-1-1-122-1-1-122-1-1-1-1-1-1000222-1-1-122-1-1-122-1-1-122-1-1-1-1-1-1000
χ7222-1-1-122-1-1-1-22-1-1-1-2-2111111000222-1-1-122-1-1-1-22-1-1-1-2-2111111000222-1-1-122-1-1-1-22-1-1-1-2-2111111000222-1-1-122-1-1-1-22-1-1-1-2-2111111000
χ8222-1-1-1-22-1-1-10-211100−i3−i3−i3i3i3i3000222-1-1-1-22-1-1-10-211100−i3−i3−i3i3i3i3000222-1-1-1-22-1-1-10-211100−i3−i3−i3i3i3i3000222-1-1-1-22-1-1-10-211100−i3−i3−i3i3i3i3000
χ9222-1-1-1-22-1-1-10-211100i3i3i3−i3−i3−i3000222-1-1-1-22-1-1-10-211100i3i3i3−i3−i3−i3000222-1-1-1-22-1-1-10-211100i3i3i3−i3−i3−i3000222-1-1-1-22-1-1-10-211100i3i3i3−i3−i3−i3000
χ1022-12-1-12-12-1-12-12-1-1-1-12-1-12-1-100022-12-1-12-12-1-12-12-1-1-1-12-1-12-1-100022-12-1-12-12-1-12-12-1-1-1-12-1-12-1-100022-12-1-12-12-1-12-12-1-1-1-12-1-12-1-1000
χ1122-12-1-12-12-1-1-2-12-1-111-211-21100022-12-1-12-12-1-1-2-12-1-111-211-21100022-12-1-12-12-1-1-2-12-1-111-211-21100022-12-1-12-12-1-1-2-12-1-111-211-211000
χ1222-12-1-1-2-12-1-101-211−i3i30−i3i30−i3i300022-12-1-1-2-12-1-101-211−i3i30−i3i30−i3i300022-12-1-1-2-12-1-101-211−i3i30−i3i30−i3i300022-12-1-1-2-12-1-101-211−i3i30−i3i30−i3i3000
χ1322-12-1-1-2-12-1-101-211i3−i30i3−i30i3−i300022-12-1-1-2-12-1-101-211i3−i30i3−i30i3−i300022-12-1-1-2-12-1-101-211i3−i30i3−i30i3−i300022-12-1-1-2-12-1-101-211i3−i30i3−i30i3−i3000
χ1422-1-12-12-1-12-12-1-12-1-1-1-12-1-1-1200022-1-12-12-1-12-12-1-12-1-1-1-12-1-1-1200022-1-12-12-1-12-12-1-12-1-1-1-12-1-1-1200022-1-12-12-1-12-12-1-12-1-1-1-12-1-1-12000
χ1522-1-12-12-1-12-1-2-1-12-1111-2111-200022-1-12-12-1-12-1-2-1-12-1111-2111-200022-1-12-12-1-12-1-2-1-12-1111-2111-200022-1-12-12-1-12-1-2-1-12-1111-2111-2000
χ1622-1-12-1-2-1-12-1011-21−i3i3i30−i3−i3i3000022-1-12-1-2-1-12-1011-21−i3i3i30−i3−i3i3000022-1-12-1-2-1-12-1011-21−i3i3i30−i3−i3i3000022-1-12-1-2-1-12-1011-21−i3i3i30−i3−i3i30000
χ1722-1-12-1-2-1-12-1011-21i3−i3−i30i3i3−i3000022-1-12-1-2-1-12-1011-21i3−i3−i30i3i3−i3000022-1-12-1-2-1-12-1011-21i3−i3−i30i3i3−i3000022-1-12-1-2-1-12-1011-21i3−i3−i30i3i3−i30000
χ1822-1-1-122-1-1-122-1-1-12-1-1-1-12-12-100022-1-1-122-1-1-122-1-1-12-1-1-1-12-12-100022-1-1-122-1-1-122-1-1-12-1-1-1-12-12-100022-1-1-122-1-1-122-1-1-12-1-1-1-12-12-1000
χ1922-1-1-122-1-1-12-2-1-1-121111-21-2100022-1-1-122-1-1-12-2-1-1-121111-21-2100022-1-1-122-1-1-12-2-1-1-121111-21-2100022-1-1-122-1-1-12-2-1-1-121111-21-21000
χ2022-1-1-12-2-1-1-120111-2−i3i3−i3i30i30−i300022-1-1-12-2-1-1-120111-2−i3i3−i3i30i30−i300022-1-1-12-2-1-1-120111-2−i3i3−i3i30i30−i300022-1-1-12-2-1-1-120111-2−i3i3−i3i30i30−i3000
χ2122-1-1-12-2-1-1-120111-2i3−i3i3−i30−i30i300022-1-1-12-2-1-1-120111-2i3−i3i3−i30−i30i300022-1-1-12-2-1-1-120111-2i3−i3i3−i30−i30i300022-1-1-12-2-1-1-120111-2i3−i3i3−i30−i30i3000
χ222-222220-2-2-2-200000000000002−202-222220-2-2-2-200000000000002−202-222220-2-2-2-200000000000002−202-222220-2-2-2-200000000000002−20
χ232-222220-2-2-2-20000000000000−2202-222220-2-2-2-20000000000000−2202-222220-2-2-2-20000000000000−2202-222220-2-2-2-20000000000000−220
χ244-44-2-2-20-422200000000000000004-44-2-2-20-422200000000000000004-44-2-2-20-422200000000000000004-44-2-2-20-42220000000000000000
χ254-4-24-2-202-42200000000000000004-4-24-2-202-42200000000000000004-4-24-2-202-42200000000000000004-4-24-2-202-4220000000000000000
χ264-4-2-24-2022-4200000000000000004-4-2-24-2022-4200000000000000004-4-2-24-2022-4200000000000000004-4-2-24-2022-420000000000000000
χ274-4-2-2-240222-400000000000000004-4-2-2-240222-400000000000000004-4-2-2-240222-400000000000000004-4-2-2-240222-40000000000000000
χ28111111111111111111111111111111111111111111111111111111−1+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+i32−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ29111111111111111111111111-1-1-1111111111111111111111111-1-1-1−1+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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−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−i32−1−i321+i321+i321+i32
χ3011111111111-11111-1-1-1-1-1-1-1-111-111111111111-11111-1-1-1-1-1-1-1-111-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32
χ3111111111111-11111-1-1-1-1-1-1-1-1-1-1111111111111-11111-1-1-1-1-1-1-1-1-1-11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+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−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32
χ32222222-222220-2-2-2-200000000000222222-222220-2-2-2-200000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i301−i31−i31−i31−i300000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i301+i31+i31+i31+i300000000000
χ33222-1-1-122-1-1-122-1-1-122-1-1-1-1-1-1000222-1-1-122-1-1-122-1-1-122-1-1-1-1-1-1000−1+i3−1+i3−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i32000−1−i3−1−i3−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i32000
χ34222-1-1-122-1-1-1-22-1-1-1-2-2111111000222-1-1-122-1-1-1-22-1-1-1-2-2111111000−1+i3−1+i3−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i3−1+i31−i321−i321−i321−i31−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32000−1−i3−1−i3−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i3−1−i31+i321+i321+i321+i31+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32000
χ35222-1-1-1-22-1-1-10-211100−i3−i3−i3i3i3i3000222-1-1-1-22-1-1-10-211100−i3−i3−i3i3i3i3000−1+i3−1+i3−1+i31−i321−i321−i321−i3−1+i31−i321−i321−i3201−i3−1+i32−1+i32−1+i32003+i323+i323+i32−3−i32−3−i32−3−i32000−1−i3−1−i3−1−i31+i321+i321+i321+i3−1−i31+i321+i321+i3201+i3−1−i32−1−i32−1−i3200−3+i32−3+i32−3+i323−i323−i323−i32000
χ36222-1-1-1-22-1-1-10-211100i3i3i3−i3−i3−i3000222-1-1-1-22-1-1-10-211100i3i3i3−i3−i3−i3000−1+i3−1+i3−1+i31−i321−i321−i321−i3−1+i31−i321−i321−i3201−i3−1+i32−1+i32−1+i3200−3−i32−3−i32−3−i323+i323+i323+i32000−1−i3−1−i3−1−i31+i321+i321+i321+i3−1−i31+i321+i321+i3201+i3−1−i32−1−i32−1−i32003−i323−i323−i32−3+i32−3+i32−3+i32000
χ3722-12-1-12-12-1-12-12-1-1-1-12-1-12-1-100022-12-1-12-12-1-12-12-1-1-1-12-1-12-1-1000−1+i3−1+i31−i32−1+i31−i321−i32−1+i31−i32−1+i31−i321−i32−1+i31−i32−1+i31−i321−i321−i321−i32−1+i31−i321−i32−1+i31−i321−i32000−1−i3−1−i31+i32−1−i31+i321+i32−1−i31+i32−1−i31+i321+i32−1−i31+i32−1−i31+i321+i321+i321+i32−1−i31+i321+i32−1−i31+i321+i32000
χ3822-12-1-12-12-1-1-2-12-1-111-211-21100022-12-1-12-12-1-1-2-12-1-111-211-211000−1+i3−1+i31−i32−1+i31−i321−i32−1+i31−i32−1+i31−i321−i321−i31−i32−1+i31−i321−i32−1+i32−1+i321−i3−1+i32−1+i321−i3−1+i32−1+i32000−1−i3−1−i31+i32−1−i31+i321+i32−1−i31+i32−1−i31+i321+i321+i31+i32−1−i31+i321+i32−1−i32−1−i321+i3−1−i32−1−i321+i3−1−i32−1−i32000
χ3922-12-1-1-2-12-1-101-211−i3i30−i3i30−i3i300022-12-1-1-2-12-1-101-211−i3i30−i3i30−i3i3000−1+i3−1+i31−i32−1+i31−i321−i321−i31−i32−1+i31−i321−i320−1+i321−i3−1+i32−1+i323+i32−3−i3203+i32−3−i3203+i32−3−i32000−1−i3−1−i31+i32−1−i31+i321+i321+i31+i32−1−i31+i321+i320−1−i321+i3−1−i32−1−i32−3+i323−i320−3+i323−i320−3+i323−i32000
χ4022-12-1-1-2-12-1-101-211i3−i30i3−i30i3−i300022-12-1-1-2-12-1-101-211i3−i30i3−i30i3−i3000−1+i3−1+i31−i32−1+i31−i321−i321−i31−i32−1+i31−i321−i320−1+i321−i3−1+i32−1+i32−3−i323+i320−3−i323+i320−3−i323+i32000−1−i3−1−i31+i32−1−i31+i321+i321+i31+i32−1−i31+i321+i320−1−i321+i3−1−i32−1−i323−i32−3+i3203−i32−3+i3203−i32−3+i32000
χ4122-1-12-12-1-12-12-1-12-1-1-1-12-1-1-1200022-1-12-12-1-12-12-1-12-1-1-1-12-1-1-12000−1+i3−1+i31−i321−i32−1+i31−i32−1+i31−i321−i32−1+i31−i32−1+i31−i321−i32−1+i31−i321−i321−i321−i32−1+i31−i321−i321−i32−1+i3000−1−i3−1−i31+i321+i32−1−i31+i32−1−i31+i321+i32−1−i31+i32−1−i31+i321+i32−1−i31+i321+i321+i321+i32−1−i31+i321+i321+i32−1−i3000
χ4222-1-12-12-1-12-1-2-1-12-1111-2111-200022-1-12-12-1-12-1-2-1-12-1111-2111-2000−1+i3−1+i31−i321−i32−1+i31−i32−1+i31−i321−i32−1+i31−i321−i31−i321−i32−1+i31−i32−1+i32−1+i32−1+i321−i3−1+i32−1+i32−1+i321−i3000−1−i3−1−i31+i321+i32−1−i31+i32−1−i31+i321+i32−1−i31+i321+i31+i321+i32−1−i31+i32−1−i32−1−i32−1−i321+i3−1−i32−1−i32−1−i321+i3000
χ4322-1-12-1-2-1-12-1011-21−i3i3i30−i3−i3i3000022-1-12-1-2-1-12-1011-21−i3i3i30−i3−i3i30000−1+i3−1+i31−i321−i32−1+i31−i321−i31−i321−i32−1+i31−i320−1+i32−1+i321−i3−1+i323+i32−3−i32−3−i3203+i323+i32−3−i320000−1−i3−1−i31+i321+i32−1−i31+i321+i31+i321+i32−1−i31+i320−1−i32−1−i321+i3−1−i32−3+i323−i323−i320−3+i32−3+i323−i320000
χ4422-1-12-1-2-1-12-1011-21i3−i3−i30i3i3−i3000022-1-12-1-2-1-12-1011-21i3−i3−i30i3i3−i30000−1+i3−1+i31−i321−i32−1+i31−i321−i31−i321−i32−1+i31−i320−1+i32−1+i321−i3−1+i32−3−i323+i323+i320−3−i32−3−i323+i320000−1−i3−1−i31+i321+i32−1−i31+i321+i31+i321+i32−1−i31+i320−1−i32−1−i321+i3−1−i323−i32−3+i32−3+i3203−i323−i32−3+i320000
χ4522-1-1-122-1-1-122-1-1-12-1-1-1-12-12-100022-1-1-122-1-1-122-1-1-12-1-1-1-12-12-1000−1+i3−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i32−1+i31−i321−i321−i321−i32−1+i31−i32−1+i31−i32000−1−i3−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i32−1−i31+i321+i321+i321+i32−1−i31+i32−1−i31+i32000
χ4622-1-1-122-1-1-12-2-1-1-121111-21-2100022-1-1-122-1-1-12-2-1-1-121111-21-21000−1+i3−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i32−1+i31−i31−i321−i321−i32−1+i3−1+i32−1+i32−1+i32−1+i321−i3−1+i321−i3−1+i32000−1−i3−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i32−1−i31+i31+i321+i321+i32−1−i3−1−i32−1−i32−1−i32−1−i321+i3−1−i321+i3−1−i32000
χ4722-1-1-12-2-1-1-120111-2−i3i3−i3i30i30−i300022-1-1-12-2-1-1-120111-2−i3i3−i3i30i30−i3000−1+i3−1+i31−i321−i321−i32−1+i31−i31−i321−i321−i32−1+i30−1+i32−1+i32−1+i321−i33+i32−3−i323+i32−3−i320−3−i3203+i32000−1−i3−1−i31+i321+i321+i32−1−i31+i31+i321+i321+i32−1−i30−1−i32−1−i32−1−i321+i3−3+i323−i32−3+i323−i3203−i320−3+i32000
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χ9366-36-3-3-6-36-3-303-633−3i33i30−3i33i30−3i33i3000-2-21-21121-2110-12-1-1i3−i30i3−i30i3−i3000000000000000000000000000000000000000000000000000000000
χ9466-36-3-3-6-36-3-303-6333i3−3i303i3−3i303i3−3i3000-2-21-21121-2110-12-1-1−i3i30−i3i30−i3i3000000000000000000000000000000000000000000000000000000000
χ9566-3-36-36-3-36-36-3-36-3-3-3-36-3-3-36000-2-211-21-211-21-211-21111-2111-2000000000000000000000000000000000000000000000000000000000
χ9666-3-36-36-3-36-3-6-3-36-3333-6333-6000-2-211-21-211-21211-21-1-1-12-1-1-12000000000000000000000000000000000000000000000000000000000
χ9766-3-36-3-6-3-36-3033-63−3i33i33i30−3i3−3i33i30000-2-211-21211-210-1-12-1i3−i3−i30i3i3−i30000000000000000000000000000000000000000000000000000000000
χ9866-3-36-3-6-3-36-3033-633i3−3i3−3i303i33i3−3i30000-2-211-21211-210-1-12-1−i3i3i30−i3−i3i30000000000000000000000000000000000000000000000000000000000
χ9966-3-3-366-3-3-366-3-3-36-3-3-3-36-36-3000-2-2111-2-2111-2-2111-21111-21-21000000000000000000000000000000000000000000000000000000000
χ10066-3-3-366-3-3-36-6-3-3-363333-63-63000-2-2111-2-2111-22111-2-1-1-1-12-12-1000000000000000000000000000000000000000000000000000000000
χ10166-3-3-36-6-3-3-360333-6−3i33i3−3i33i303i30−3i3000-2-2111-22111-20-1-1-12i3−i3i3−i30−i30i3000000000000000000000000000000000000000000000000000000000
χ10266-3-3-36-6-3-3-360333-63i3−3i33i3−3i30−3i303i3000-2-2111-22111-20-1-1-12−i3i3−i3i30i30−i3000000000000000000000000000000000000000000000000000000000
χ1036-666660-6-6-6-6000000000000032−320-22-2-2-2-2022220000000000000−220000000000000000000000000000000000000000000000000000000
χ1046-666660-6-6-6-60000000000000−32320-22-2-2-2-20222200000000000002−20000000000000000000000000000000000000000000000000000000
χ10512-1212-6-6-60-126660000000000000000-44-422204-2-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10612-12-612-6-606-12660000000000000000-442-4220-24-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10712-12-6-612-6066-1260000000000000000-4422-420-2-24-20000000000000000000000000000000000000000000000000000000000000000000000
χ10812-12-6-6-6120666-120000000000000000-44222-40-2-2-240000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.