Finite Group Databasebeta

← Group #13166265

Character table — Group #13166265

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size112222233444444444444444444466688888888888888889912121212121212121212121212121212181818181827273636363636363654545472727272108108108108
order12346884433661212121212242424242424242424242883366121212122424242424242424446666121212122424242424242424288121222688882424488242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1ii−i−iii−i−i
χ411111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1−i−iii−i−iii
χ51111111-1-11111111111111111111-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111111-1-1-11111-1-1-1-1
χ61111111-1-11111111111111111111-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-1-1-111-1-1-1-1-1-1-11111
χ71111111-1-11111111111111111111-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1ii−i−i-1-1111ii−i−i−i−iii
χ81111111-1-11111111111111111111-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1−i−iii-1-1111−i−iiiii−i−i
χ911111-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1111111-11-1-1-11-1-11-11-11-11-1
χ1011111-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-111111-11-11-1-11-1-1-11-11-11-11
χ1111111-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1i−i−ii11-111i−i−iii−i−ii
χ1211111-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1−iii−i11-111−iii−i−iii−i
χ1311111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-111-1-111-11-1-1-1-1111-11-1-11-11
χ1411111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-111-1-11-11-11-1-1-111-11-111-11-1
χ1511111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-111-1i−i−ii111-1-1i−i−ii−iii−i
χ1611111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-111-1−iii−i111-1-1−iii−ii−i−ii
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χ20222-2200-2-22222-2-2-2-2-200000000002002222-2-2-2-200000000-2-22222-2-2-2-200000000200-2-2222000000-20000000000
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χ848-8-4044i2−4i2002-4-24−6i6i000−2ζ+4ζ34ζ−2ζ3−2i2−2i22ζ−4ζ3−4ζ+2ζ32i22i2−2i22i2000-121-23i−3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i20000000000000000000000000000000000000000000
χ858-8-4044i2−4i200-424-2006i−6i0−2i2−2i24ζ−2ζ3−2ζ+4ζ32i22i2−4ζ+2ζ32ζ−4ζ3−2i22i20002-1-2100−3i3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ30000000000000000000000000000000000000000000
χ868-8-4044i2−4i200-424-200−6i6i0−2i2−2i2−2ζ+4ζ34ζ−2ζ32i22i22ζ−4ζ3−4ζ+2ζ3−2i22i20002-1-21003i−3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ30000000000000000000000000000000000000000000
χ878-8-404−4i24i2002-4-246i−6i000−4ζ+2ζ32ζ−4ζ32i22i24ζ−2ζ3−2ζ+4ζ3−2i2−2i22i2−2i2000-121-2−3i3i002ζ−ζ3−ζ+2ζ3−i2−i2−2ζ+ζ3ζ−2ζ3i2i20000000000000000000000000000000000000000000
χ888-8-404−4i24i2002-4-24−6i6i0002ζ−4ζ3−4ζ+2ζ32i22i2−2ζ+4ζ34ζ−2ζ3−2i2−2i22i2−2i2000-121-23i−3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i20000000000000000000000000000000000000000000
χ898-8-404−4i24i200-424-2006i−6i02i22i2−4ζ+2ζ32ζ−4ζ3−2i2−2i24ζ−2ζ3−2ζ+4ζ32i2−2i20002-1-2100−3i3i−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ30000000000000000000000000000000000000000000
χ908-8-404−4i24i200-424-200−6i6i02i22i22ζ−4ζ3−4ζ+2ζ3−2i2−2i2−2ζ+4ζ34ζ−2ζ32i2−2i20002-1-21003i−3i−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ30000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.