Finite Group DatabasebetaFinite Group Databasebeta| order | 9516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D39⋊D61 |
| unambiguous semidirect product | D183⋊D13 |
| unambiguous semidirect product | D793⋊D3 |
| Fitting, socle, derived, Hall | C3×C13×C61 ⋊ C22 |
| Hall | C13×C61 ⋊ C2×D3 |
| Hall | C3×C61 ⋊ C2×D13 |
| Sylow | C61 ⋊ D3×D13 |
| Hall | C3×C13 ⋊ C2×D61 |
| Sylow | C13 ⋊ D3×D61 |
| Sylow | C3 ⋊ D13×D61 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13×C61 | C22 |
| LCS | G ▷ C3×C13×C61 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,13,61|d^a=d^12,e^a=e^60,c^b=c^2,d^b=d^12654 conjugacy classes — view the full character table.
| maximal subgroup of | D117⋊D61, #18011732⋊D3, #18011731⋊D3, … |
| maximal normal subgroup of | #18011732⋊D3, #18011731⋊D3, (C3⋊(D13⋊C3))⋊D61, … |
| maximal quotient of | D117⋊D61, C3×D39⋊D61, D183⋊D39, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 84);