Finite Group Databasebeta

← Group #13165969

Character table — Group #13165969

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111222222222222222266666688889999121212121212121212121212121212121212121212121212121216161616161616161616161616161616242424242424242454545454545472727272108108
order1244333366661212121212121212248888361212888824666612121212242424242424242424242424242424243333666612121212121212126666121212124444882424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ41111111111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ511-1-111111111-1-1-1-1-1-1-1-1-1111-1-111-1-1ii−i−i1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−ii−iii−i−ii−i
χ611-1-111111111-1-1-1-1-1-1-1-1-1111-1-111-1-1−i−iii1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−ii−i−iii−ii
χ711-1-111111111-1-1-1-1-1-1-1-1-11-1-11111-1-1ii−i−i-11-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiii−iii−i−i−ii
χ811-1-111111111-1-1-1-1-1-1-1-1-11-1-11111-1-1−i−iii-11-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−ii−i−iiii−i
χ922222222222222222222220000-1-1-1-1222200222222220000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-100
χ1022222222222222222222220000-1-1-1-1-2-2-2-200222222220000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2111100
χ1122222-1-1-12-1-1-122-1-1-1-1-1-122222222220000222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-12-1-1-12-1-1-1000000000000
χ1222222-1-1-12-1-1-122-1-1-1-1-1-122-2-2-2-222220000-2-22-1-1-12-1-1-1-2-2111111-2-21111112-1-1-12-1-1-122-1-1-1-1-1-1-2111-2111000000000000
χ132222-12-1-1-12-1-1-1-122-1-1-1-12222222222000022-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-12-1-1000000000000
χ142222-12-1-1-12-1-1-1-122-1-1-1-122-2-2-2-222220000-2-2-12-1-1-12-1-111-2-2111111-2-21111-12-1-1-12-1-1-1-122-1-1-1-11-2111-211000000000000
χ152222-1-12-1-1-12-1-1-1-1-122-1-12222222222000022-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1-1-12-1000000000000
χ162222-1-12-1-1-12-1-1-1-1-122-1-122-2-2-2-222220000-2-2-1-12-1-1-12-11111-2-2111111-2-211-1-12-1-1-12-1-1-1-1-122-1-111-2111-21000000000000
χ172222-1-1-12-1-1-12-1-1-1-1-1-1222222222222000022-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12000000000000
χ182222-1-1-12-1-1-12-1-1-1-1-1-12222-2-2-2-222220000-2-2-1-1-12-1-1-12111111-2-2111111-2-2-1-1-12-1-1-12-1-1-1-1-1-122111-2111-2000000000000
χ1922-2-222222222-2-2-2-2-2-2-2-2-220000-1-1112i2i−2i−2i00-2-2-2-222220000000000000000-1-1-1-1-1-1-1-1111111110000000000002i−2i−i−iii00
χ2022-2-222222222-2-2-2-2-2-2-2-2-220000-1-111−2i−2i2i2i00-2-2-2-222220000000000000000-1-1-1-1-1-1-1-111111111000000000000−2i2iii−i−i00
χ2122-2-22-1-1-12-1-1-1-2-2111111-2222-2-222-2-200002-2-21112-1-1-122-1-1-1-1-1-1-2-21111112-1-1-12-1-1-1-2-21111112-1-1-1-2111000000000000
χ2222-2-22-1-1-12-1-1-1-2-2111111-22-2-22222-2-20000-22-21112-1-1-1-2-211111122-1-1-1-1-1-12-1-1-12-1-1-1-2-2111111-21112-1-1-1000000000000
χ2322-2-2-12-1-1-12-1-111-2-21111-2222-2-222-2-200002-21-211-12-1-1-1-122-1-1-1-111-2-21111-12-1-1-12-1-111-2-21111-12-1-11-211000000000000
χ2422-2-2-12-1-1-12-1-111-2-21111-22-2-22222-2-20000-221-211-12-1-111-2-21111-1-122-1-1-1-1-12-1-1-12-1-111-2-211111-211-12-1-1000000000000
χ2522-2-2-1-12-1-1-12-11111-2-211-2222-2-222-2-200002-211-21-1-12-1-1-1-1-122-1-11111-2-211-1-12-1-1-12-11111-2-211-1-12-111-21000000000000
χ2622-2-2-1-12-1-1-12-11111-2-211-22-2-22222-2-20000-2211-21-1-12-11111-2-211-1-1-1-122-1-1-1-12-1-1-12-11111-2-21111-21-1-12-1000000000000
χ2722-2-2-1-1-12-1-1-12111111-2-2-2222-2-222-2-200002-2111-2-1-1-12-1-1-1-1-1-122111111-2-2-1-1-12-1-1-12111111-2-2-1-1-12111-2000000000000
χ2822-2-2-1-1-12-1-1-12111111-2-2-22-2-22222-2-20000-22111-2-1-1-12111111-2-2-1-1-1-1-1-122-1-1-12-1-1-12111111-2-2111-2-1-1-12000000000000
χ292-22i−2i2222-2-2-2-22i−2i2i−2i2i−2i2i−2i00i2−i22−2-11i−i2ζ−2ζ2ζ3−2ζ30000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−2-1-1-1-11111i−ii−ii−ii−i000000001−i−1+i1+i−1−i00ζ−ζζ3−ζ300
χ302-22i−2i2222-2-2-2-22i−2i2i−2i2i−2i2i−2i00i2−i22−2-11i−i−2ζ2ζ−2ζ32ζ30000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−2-1-1-1-11111i−ii−ii−ii−i00000000−1+i1−i−1−i1+i00−ζζ−ζ3ζ300
χ312-22i−2i2222-2-2-2-22i−2i2i−2i2i−2i2i−2i00−i2i2−22-11i−i2ζ−2ζ2ζ3−2ζ30000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−22-1-1-1-11111i−ii−ii−ii−i00000000−1+i1−i−1−i1+i00ζ−ζζ3−ζ300
χ322-22i−2i2222-2-2-2-22i−2i2i−2i2i−2i2i−2i00−i2i2−22-11i−i−2ζ2ζ−2ζ32ζ30000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−22-1-1-1-11111i−ii−ii−ii−i000000001−i−1+i1+i−1−i00−ζζ−ζ3ζ300
χ332-2−2i2i2222-2-2-2-2−2i2i−2i2i−2i2i−2i2i00i2−i2−22-11−ii2ζ3−2ζ32ζ−2ζ0000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−22-1-1-1-11111−ii−ii−ii−ii000000001+i−1−i1−i−1+i00ζ3−ζ3ζ−ζ00
χ342-2−2i2i2222-2-2-2-2−2i2i−2i2i−2i2i−2i2i00i2−i2−22-11−ii−2ζ32ζ3−2ζ2ζ0000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−22-1-1-1-11111−ii−ii−ii−ii00000000−1−i1+i−1+i1−i00−ζ3ζ3−ζζ00
χ352-2−2i2i2222-2-2-2-2−2i2i−2i2i−2i2i−2i2i00−i2i22−2-11−ii2ζ3−2ζ32ζ−2ζ0000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−2-1-1-1-11111−ii−ii−ii−ii00000000−1−i1+i−1+i1−i00ζ3−ζ3ζ−ζ00
χ362-2−2i2i2222-2-2-2-2−2i2i−2i2i−2i2i−2i2i00−i2i22−2-11−ii−2ζ32ζ3−2ζ2ζ0000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−2-1-1-1-11111−ii−ii−ii−ii000000001+i−1−i1−i−1+i00−ζ3ζ3−ζζ00
χ3733333333333333333333-1-1111100003333-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-1-1-1-1-1-1-1-11111-1-10000-1-1
χ3833333333333333333333-1-111110000-3-3-3-3-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-1-1-1-1-1-1-1-1-1-1-1-111000011
χ3933333333333333333333-1-1-1-1-1-10000333311-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000011111111-1-1-1-1-1-1000011
χ4033333333333333333333-1-1-1-1-1-10000-3-3-3-311-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000111111111111110000-1-1
χ4133-3-333333333-3-3-3-3-3-3-3-31-111-1-100003i3i−3i−3i-111111-1-1-1-111111111-1-1-1-1-1-1-1-10000000000000000-1-1-1-11111ii−i−i−ii0000−ii
χ4233-3-333333333-3-3-3-3-3-3-3-31-111-1-10000−3i−3i3i3i-111111-1-1-1-111111111-1-1-1-1-1-1-1-10000000000000000-1-1-1-11111−i−iiii−i0000i−i
χ4333-3-333333333-3-3-3-3-3-3-3-31-1-1-11100003i3i−3i−3i1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000001111-1-1-1-1−i−iii−ii0000i−i
χ4433-3-333333333-3-3-3-3-3-3-3-31-1-1-1110000−3i−3i3i3i1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000001111-1-1-1-1ii−i−ii−i0000−ii
χ4544444-2-2-24-2-2-244-2-2-2-2-2-2440000-2-2-2-20000004-2-2-24-2-2-20000000000000000-2111-2111-2-211111100000000000000000000
χ464444-24-2-2-24-2-2-2-244-2-2-2-2440000-2-2-2-2000000-24-2-2-24-2-200000000000000001-2111-21111-2-2111100000000000000000000
χ474444-2-24-2-2-24-2-2-2-2-244-2-2440000-2-2-2-2000000-2-24-2-2-24-2000000000000000011-2111-211111-2-21100000000000000000000
χ484444-2-2-24-2-2-24-2-2-2-2-2-244440000-2-2-2-2000000-2-2-24-2-2-240000000000000000111-2111-2111111-2-200000000000000000000
χ4944-4-44-2-2-24-2-2-2-4-4222222-440000-2-222000000-42224-2-2-20000000000000000-2111-211122-1-1-1-1-1-100000000000000000000
χ5044-4-4-24-2-2-24-2-222-4-42222-440000-2-2220000002-422-24-2-200000000000000001-2111-211-1-122-1-1-1-100000000000000000000
χ5144-4-4-2-24-2-2-24-22222-4-422-440000-2-22200000022-42-2-24-2000000000000000011-2111-21-1-1-1-122-1-100000000000000000000
χ5244-4-4-2-2-24-2-2-24222222-4-4-440000-2-222000000222-4-2-2-240000000000000000111-2111-2-1-1-1-1-1-12200000000000000000000
χ534-44i−4i4444-4-4-4-44i−4i4i−4i4i−4i4i−4i0000001-1−ii4ζ−4ζ4ζ3−4ζ3000000000000000000000000001111-1-1-1-1−ii−ii−ii−ii00000000000000−ζζ−ζ3ζ300
χ544-44i−4i4444-4-4-4-44i−4i4i−4i4i−4i4i−4i0000001-1−ii−4ζ4ζ−4ζ34ζ3000000000000000000000000001111-1-1-1-1−ii−ii−ii−ii00000000000000ζ−ζζ3−ζ300
χ554-44i−4i4-2-2-2-42224i−4i−2i2i−2i2i−2i2i002i2−2i222−22-222i−2i000000000000002i2−2i2−i2i2−i2i2−i2i222−22−22−22−22-21112-1-1-12i−2i−ii−ii−ii00000000000000000000
χ564-44i−4i4-2-2-2-42224i−4i−2i2i−2i2i−2i2i00−2i22i2−2222-222i−2i00000000000000−2i22i2i2−i2i2−i2i2−i2−22222−22−22−2-21112-1-1-12i−2i−ii−ii−ii00000000000000000000
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χ714-4−4i4i-2-2-24222-42i−2i2i−2i2i−2i−4i4i002i2−2i2−2222-22−2i2i00000000000000−i2i2−i2i2−i2i22i2−2i22−22−22−2−2222111-2-1-1-12i−ii−ii−i−2i2i00000000000000000000
χ724-4−4i4i-2-2-24222-42i−2i2i−2i2i−2i−4i4i00−2i22i222−22-22−2i2i00000000000000i2−i2i2−i2i2−i2−2i22i2−22−22−2222−22111-2-1-1-12i−ii−ii−i−2i2i00000000000000000000
χ7366666-3-3-36-3-3-366-3-3-3-3-3-3-2-2222200000000-2-2-2111-211122-1-1-1-1-1-122-1-1-1-1-1-10000000000000000-2111-2111000000000000
χ7466666-3-3-36-3-3-366-3-3-3-3-3-3-2-2-2-2-2-20000000022-2111-2111-2-2111111-2-211111100000000000000002-1-1-12-1-1-1000000000000
χ756666-36-3-3-36-3-3-3-366-3-3-3-3-2-2222200000000-2-21-2111-211-1-122-1-1-1-1-1-122-1-1-1-100000000000000001-2111-211000000000000
χ766666-36-3-3-36-3-3-3-366-3-3-3-3-2-2-2-2-2-200000000221-2111-21111-2-2111111-2-211110000000000000000-12-1-1-12-1-1000000000000
χ776666-3-36-3-3-36-3-3-3-3-366-3-3-2-2222200000000-2-211-2111-21-1-1-1-122-1-1-1-1-1-122-1-1000000000000000011-2111-21000000000000
χ786666-3-36-3-3-36-3-3-3-3-366-3-3-2-2-2-2-2-2000000002211-2111-211111-2-2111111-2-2110000000000000000-1-12-1-1-12-1000000000000
χ796666-3-3-36-3-3-36-3-3-3-3-3-366-2-2222200000000-2-2111-2111-2-1-1-1-1-1-122-1-1-1-1-1-1220000000000000000111-2111-2000000000000
χ806666-3-3-36-3-3-36-3-3-3-3-3-366-2-2-2-2-2-20000000022111-2111-2111111-2-2111111-2-20000000000000000-1-1-12-1-1-12000000000000
χ8166-6-66-3-3-36-3-3-3-6-63333332-222-2-200000000-222-1-1-1-211122-1-1-1-1-1-1-2-21111110000000000000000-21112-1-1-1000000000000
χ8266-6-66-3-3-36-3-3-3-6-63333332-2-2-222000000002-22-1-1-1-2111-2-211111122-1-1-1-1-1-100000000000000002-1-1-1-2111000000000000
χ8366-6-6-36-3-3-36-3-333-6-633332-222-2-200000000-22-12-1-11-211-1-122-1-1-1-111-2-2111100000000000000001-211-12-1-1000000000000
χ8466-6-6-36-3-3-36-3-333-6-633332-2-2-222000000002-2-12-1-11-21111-2-21111-1-122-1-1-1-10000000000000000-12-1-11-211000000000000
χ8566-6-6-3-36-3-3-36-33333-6-6332-222-2-200000000-22-1-12-111-21-1-1-1-122-1-11111-2-211000000000000000011-21-1-12-1000000000000
χ8666-6-6-3-36-3-3-36-33333-6-6332-2-2-222000000002-2-1-12-111-211111-2-211-1-1-1-122-1-10000000000000000-1-12-111-21000000000000
χ8766-6-6-3-3-36-3-3-36333333-6-62-222-2-200000000-22-1-1-12111-2-1-1-1-1-1-122111111-2-20000000000000000111-2-1-1-12000000000000
χ8866-6-6-3-3-36-3-3-36333333-6-62-2-2-222000000002-2-1-1-12111-2111111-2-2-1-1-1-1-1-1220000000000000000-1-1-12111-2000000000000
χ898-88i−8i8-4-4-4-84448i−8i−4i4i−4i4i−4i4i0000002-2−2i2i0000000000000000000000000000002-1-1-1-2111−2i2ii−ii−ii−i00000000000000000000
χ908-88i−8i-48-4-44-844−4i4i8i−8i−4i4i−4i4i0000002-2−2i2i000000000000000000000000000000-12-1-11-211i−i−2i2ii−ii−i00000000000000000000
χ918-88i−8i-4-48-444-84−4i4i−4i4i8i−8i−4i4i0000002-2−2i2i000000000000000000000000000000-1-12-111-21i−ii−i−2i2ii−i00000000000000000000
χ928-88i−8i-4-4-48444-8−4i4i−4i4i−4i4i8i−8i0000002-2−2i2i000000000000000000000000000000-1-1-12111-2i−ii−ii−i−2i2i00000000000000000000
χ938-8−8i8i8-4-4-4-8444−8i8i4i−4i4i−4i4i−4i0000002-22i−2i0000000000000000000000000000002-1-1-1-21112i−2i−ii−ii−ii00000000000000000000
χ948-8−8i8i-48-4-44-8444i−4i−8i8i4i−4i4i−4i0000002-22i−2i000000000000000000000000000000-12-1-11-211−ii2i−2i−ii−ii00000000000000000000
χ958-8−8i8i-4-48-444-844i−4i4i−4i−8i8i4i−4i0000002-22i−2i000000000000000000000000000000-1-12-111-21−ii−ii2i−2i−ii00000000000000000000
χ968-8−8i8i-4-4-48444-84i−4i4i−4i4i−4i−8i8i0000002-22i−2i000000000000000000000000000000-1-1-12111-2−ii−ii−ii2i−2i00000000000000000000

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