Finite Group Databasebeta

← Group #11722199

Character table — Group #11722199

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size112222222222222222222222222222244444444444444444444444444444444444444488888888888888888888888888854545454216
order123333333333333466666666666668812121212121212121212121212242424242424242424242424242424242424242424242424242441212121212121212121212121212121212121212121212121212161616164
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1
χ41111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11
χ522222222222222222222222222222-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ6222222222222222-2222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000000000022−2−20
χ7222222222222222-2222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000000−2−2220
χ8222222-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000
χ9222222-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-211111111111111111100000
χ10222222-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-2-22222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111111000000000−i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3i300000
χ11222222-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-2-22222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111111000000000i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3−i300000
χ12222-1-1-1222-1-1-1-1-1-122-1-1-1222-1-1-1-1-1-1222-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-100000
χ13222-1-1-1222-1-1-1-1-1-122-1-1-1222-1-1-1-1-1-1222-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2111111-2-2-2111111-2-2-211111100000
χ14222-1-1-1222-1-1-1-1-1-122-1-1-1222-1-1-1-1-1-1-2-22-1-1-1222-1-1-1-1-1-1-2-2111111-2-2-2-2-2-2111111111111000−i3−i3−i3i3i3i3000−i3−i3−i3i3i3i3000−i3−i3−i3i3i3i300000
χ15222-1-1-1222-1-1-1-1-1-122-1-1-1222-1-1-1-1-1-1-2-22-1-1-1222-1-1-1-1-1-1-2-2111111-2-2-2-2-2-2111111111111000i3i3i3−i3−i3−i3000i3i3i3−i3−i3−i3000i3i3i3−i3−i3−i300000
χ16222-1-1-1-1-1-1222-1-1-122-1-1-1-1-1-1222-1-1-1222-1-1-1-1-1-1222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-122200000
χ17222-1-1-1-1-1-1222-1-1-122-1-1-1-1-1-1222-1-1-1222-1-1-1-1-1-1222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-2-2-2111111111-2-2-2111111111-2-2-200000
χ18222-1-1-1-1-1-1222-1-1-122-1-1-1-1-1-1222-1-1-1-2-22-1-1-1-1-1-1222-1-1-1-2-2111111111111-2-2-2-2-2-2111111000−i3−i3−i3i3i3i3i3i3i3000−i3−i3−i3−i3−i3−i3i3i3i300000000
χ19222-1-1-1-1-1-1222-1-1-122-1-1-1-1-1-1222-1-1-1-2-22-1-1-1-1-1-1222-1-1-1-2-2111111111111-2-2-2-2-2-2111111000i3i3i3−i3−i3−i3−i3−i3−i3000i3i3i3i3i3i3−i3−i3−i300000000
χ20222-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1222-1-1-100000
χ21222-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2111111111111-2-2-2111-2-2-211100000
χ22222-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1222-2-22-1-1-1-1-1-1-1-1-1222-2-2111111111111111111-2-2-2-2-2-2000−i3−i3−i3i3i3i3−i3−i3−i3i3i3i3000i3i3i3000−i3−i3−i300000
χ23222-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1222-2-22-1-1-1-1-1-1-1-1-1222-2-2111111111111111111-2-2-2-2-2-2000i3i3i3−i3−i3−i3i3i3i3−i3−i3−i3000−i3−i3−i3000i3i3i300000
χ2422-12-1-12-1-12-1-12-1-12-12-1-12-1-12-1-12-1-122-12-1-12-1-12-1-12-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12-1-12-1-12-1-12-1-12-1-12-1-12-1-12-1-12-1-100000
χ2522-12-1-12-1-12-1-12-1-12-12-1-12-1-12-1-12-1-122-12-1-12-1-12-1-12-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-211-211-211-211-211-211-211-211-21100000
χ2622-12-1-12-1-12-1-12-1-12-12-1-12-1-12-1-12-1-1-2-2-12-1-12-1-12-1-12-1-111-2-21111-2-21111-2-21111-2-211110−i3i30−i3i30−i3i30−i3i30−i3i30−i3i30−i3i30−i3i30−i3i300000
χ2722-12-1-12-1-12-1-12-1-12-12-1-12-1-12-1-12-1-1-2-2-12-1-12-1-12-1-12-1-111-2-21111-2-21111-2-21111-2-211110i3−i30i3−i30i3−i30i3−i30i3−i30i3−i30i3−i30i3−i30i3−i300000
χ2822-12-1-1-12-1-12-1-12-12-12-1-1-12-1-12-1-12-122-12-1-1-12-1-12-1-12-1-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-12-1-12-1-12-1-1-12-1-12-1-12-1-1-12-1-12-1-1200000
χ2922-12-1-1-12-1-12-1-12-12-12-1-1-12-1-12-1-12-122-12-1-1-12-1-12-1-12-1-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-211-211-2111-211-211-2111-211-211-200000
χ3022-12-1-1-12-1-12-1-12-12-12-1-1-12-1-12-1-12-1-2-2-12-1-1-12-1-12-1-12-111-2-2111111-2-21111-2-21111-2-2110−i3i30−i3i30−i3i3i30−i3i30−i3i30−i3−i3i30−i3i30−i3i3000000
χ3122-12-1-1-12-1-12-1-12-12-12-1-1-12-1-12-1-12-1-2-2-12-1-1-12-1-12-1-12-111-2-2111111-2-21111-2-21111-2-2110i3−i30i3−i30i3−i3−i30i3−i30i3−i30i3i3−i30i3−i30i3−i3000000
χ3222-12-1-1-1-12-1-12-1-122-12-1-1-1-12-1-12-1-1222-12-1-1-1-12-1-12-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1222-1-12-1-12-1-1-1-12-1-12-1-12-12-1-12-1-12-100000
χ3322-12-1-1-1-12-1-12-1-122-12-1-1-1-12-1-12-1-1222-12-1-1-1-12-1-12-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-211-211-21111-211-211-21-211-211-2100000
χ3422-12-1-1-1-12-1-12-1-122-12-1-1-1-12-1-12-1-12-2-2-12-1-1-1-12-1-12-1-1211-2-211111111-2-21111-2-21111-2-20−i3i30−i3i30−i3i3−i3i30−i3i30−i3i30i30−i3i30−i3i30−i300000
χ3522-12-1-1-1-12-1-12-1-122-12-1-1-1-12-1-12-1-12-2-2-12-1-1-1-12-1-12-1-1211-2-211111111-2-21111-2-21111-2-20i3−i30i3−i30i3−i3i3−i30i3−i30i3−i30−i30i3−i30i3−i30i300000
χ3622-1-12-12-1-1-12-1-1-122-1-12-12-1-1-12-1-1-1222-1-12-12-1-1-12-1-1-12-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1222-1-1-12-1-1-122-1-1-12-1-1-122-1-1-12-1-1-1200000
χ3722-1-12-12-1-1-12-1-1-122-1-12-12-1-1-12-1-1-1222-1-12-12-1-1-12-1-1-12-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-122-2111-2111-2-2111-2111-2-2111-2111-200000
χ3822-1-12-12-1-1-12-1-1-122-1-12-12-1-1-12-1-1-12-2-2-1-12-12-1-1-12-1-1-121111-2-211-2-2111111-2-2111111-2-20−i3i3i30−i3−i3i300−i3i3i30−i3−i3i300−i3i3i30−i3−i3i3000000
χ3922-1-12-12-1-1-12-1-1-122-1-12-12-1-1-12-1-1-12-2-2-1-12-12-1-1-12-1-1-121111-2-211-2-2111111-2-2111111-2-20i3−i3−i30i3i3−i300i3−i3−i30i3i3−i300i3−i3−i30i3i3−i3000000
χ4022-1-12-1-12-1-1-122-1-12-1-12-1-12-1-1-122-1-122-1-12-1-12-1-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-12222-1-1-1-12-1-1-12-1-1-12-12-1-1-122-1-1-1-122-1-1-12-100000
χ4122-1-12-1-12-1-1-122-1-12-1-12-1-12-1-1-122-1-122-1-12-1-12-1-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-2111-2111-21-2111-2-21111-2-2111-2100000
χ4222-1-12-1-12-1-1-122-1-12-1-12-1-12-1-1-122-1-1-2-2-1-12-1-12-1-1-122-1-11111-2-21111-2-2111111-2-2-2-211110−i3i3i30−i3−i3i30i30−i3−i3i300−i3i3−i3i300−i3i3i30−i300000
χ4322-1-12-1-12-1-1-122-1-12-1-12-1-12-1-1-122-1-1-2-2-1-12-1-12-1-1-122-1-11111-2-21111-2-2111111-2-2-2-211110i3−i3−i30i3i3−i30−i30i3i3−i300i3−i3i3−i300i3−i3−i30i300000
χ4422-1-12-1-1-122-1-1-12-12-1-12-1-1-122-1-1-12-122-1-12-1-1-122-1-1-12-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-122-1-12-1-1-12-1-1-12-1-122-1-1-12-1-12-1-1-122-1-100000
χ4522-1-12-1-1-122-1-1-12-12-1-12-1-1-122-1-1-12-122-1-12-1-1-122-1-1-12-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-2111-2111-211-2-2111-211-2111-2-21100000
χ4622-1-12-1-1-122-1-1-12-12-1-12-1-1-122-1-1-12-1-2-2-1-12-1-1-122-1-1-12-11111-2-2111111-2-2-2-2111111-2-2110−i3i3i30−i3−i3i30−i3i300−i3i3i30−i3i30−i3−i3i300−i3i300000
χ4722-1-12-1-1-122-1-1-12-12-1-12-1-1-122-1-1-12-1-2-2-1-12-1-1-122-1-1-12-11111-2-2111111-2-2-2-2111111-2-2110i3−i3−i30i3i3−i30i3−i300i3−i3−i30i3−i30i3i3−i300i3−i300000
χ4822-1-1-122-1-1-1-12-12-12-1-1-122-1-1-1-12-12-122-1-1-122-1-1-1-12-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-122-1-12-1-1-1-12-12-12-1-1-1-12-12-12-1-1-1-12-12-100000
χ4922-1-1-122-1-1-1-12-12-12-1-1-122-1-1-1-12-12-122-1-1-122-1-1-1-12-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-122-1-1-21111-21-21-21111-21-21-21111-21-2100000
χ5022-1-1-122-1-1-1-12-12-12-1-1-122-1-1-1-12-12-1-2-2-1-1-122-1-1-1-12-12-1111111-2-2-2-211111111-2-211-2-2110−i3i3−i3i30i30−i30−i3i3−i3i30i30−i30−i3i3−i3i30i30−i300000
χ5122-1-1-122-1-1-1-12-12-12-1-1-122-1-1-1-12-12-1-2-2-1-1-122-1-1-1-12-12-1111111-2-2-2-211111111-2-211-2-2110i3−i3i3−i30−i30i30i3−i3i3−i30−i30i30i3−i3i3−i30−i30i300000
χ5222-1-1-12-12-12-1-1-1-122-1-1-12-12-12-1-1-1-1222-1-1-12-12-12-1-1-1-12-1-1-1-1-1-122-1-122-1-122-1-1-1-1-1-1-1-1222-1-1-1-12-12-1-12-12-1-1-1-12-1-12-12-12-1-100000
χ5322-1-1-12-12-12-1-1-1-122-1-1-12-12-12-1-1-1-1222-1-1-12-12-12-1-1-1-12-1-1-1-1-1-122-1-122-1-122-1-1-1-1-1-1-1-122-21111-21-211-21-21111-211-21-21-21100000
χ5422-1-1-12-12-12-1-1-1-122-1-1-12-12-12-1-1-1-12-2-2-1-1-12-12-12-1-1-1-12111111-2-211-2-211-2-211111111-2-20−i3i3−i3i30i30−i3i30−i30−i3i3−i3i30−i3i30i30−i30−i3i300000
χ5522-1-1-12-12-12-1-1-1-122-1-1-12-12-12-1-1-1-12-2-2-1-1-12-12-12-1-1-1-12111111-2-211-2-211-2-211111111-2-20i3−i3i3−i30−i30i3−i30i30i3−i3i3−i30i3−i30−i30i30i3−i300000
χ5622-1-1-12-1-12-12-12-1-12-1-1-12-1-12-12-12-1-122-1-1-12-1-12-12-12-1-1-1-1-1-1-1-122-1-1-1-122-1-122-1-122-1-1-1-12-1-1-1-12-12-1-1-12-12-12-1-1-12-12-1-1-1-1200000
χ5722-1-1-12-1-12-12-12-1-12-1-1-12-1-12-12-12-1-122-1-1-12-1-12-12-12-1-1-1-1-1-1-1-122-1-1-1-122-1-122-1-122-1-1-1-1-21111-21-2111-21-21-2111-21-21111-200000
χ5822-1-1-12-1-12-12-12-1-12-1-1-12-1-12-12-12-1-1-2-2-1-1-12-1-12-12-12-1-1111111-2-21111-2-211-2-211-2-211110−i3i3−i3i30i30−i3−i3i30i30−i30−i3i3i30−i30−i3i3−i3i3000000
χ5922-1-1-12-1-12-12-12-1-12-1-1-12-1-12-12-12-1-1-2-2-1-1-12-1-12-12-12-1-1111111-2-21111-2-211-2-211-2-211110i3−i3i3−i30−i30i3i3−i30−i30i30i3−i3−i30i30i3−i3i3−i3000000
χ602-222222222222220-2-2-2-2-2-2-2-2-2-2-2-2-22−200000000000002−22−22−22−22−22−22−22−22−22−22−22−22−2000000000000000000000000000−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430
χ612-222222222222220-2-2-2-2-2-2-2-2-2-2-2-2-22−200000000000002−22−22−22−22−22−22−22−22−22−22−22−22−2000000000000000000000000000ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430
χ622-222222222222220-2-2-2-2-2-2-2-2-2-2-2-2-2−220000000000000−22−22−22−22−22−22−22−22−22−22−22−22−22000000000000000000000000000ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470
χ632-222222222222220-2-2-2-2-2-2-2-2-2-2-2-2-2−220000000000000−22−22−22−22−22−22−22−22−22−22−22−22−22000000000000000000000000000−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470
χ64444444-2-2-2-2-2-2-2-2-2-44444-2-2-2-2-2-2-2-2-200-4-4-4-42222222220000000000000000000000000000000000000000000000000000000000
χ65444-2-2-2444-2-2-2-2-2-2-44-2-2-2444-2-2-2-2-2-200-4222-4-4-42222220000000000000000000000000000000000000000000000000000000000
χ66444-2-2-2-2-2-2444-2-2-2-44-2-2-2-2-2-2444-2-2-200-4222222-4-4-42220000000000000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.