Finite Group DatabasebetaFinite Group Databasebeta| order | 9516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #18011723⋊C2 |
| unambiguous semidirect product | #18011727⋊C2 |
| unambiguous semidirect product | #18011731⋊C2 |
| Fitting, socle, derived, Hall | C13×C61 ⋊ C22×C3 |
| Hall | D13×D61 ⋊ C3 |
| Hall | #14558652 ⋊ C22 |
| Sylow | C61 ⋊ C2×D13⋊C3 |
| Sylow | C13 ⋊ C2×D61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C61 | C22×C3 |
| LCS | G ▷ C13×C61 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,13,61|e^a=e^60,d^b=d^12,d^c=d^3,e^c=e^4796 conjugacy classes — view the full character table.
| maximal subgroup of | D13⋊C3×D61⋊C3, C3×#18011723⋊C2, #18011723⋊D3, … |
| maximal normal subgroup of | D13⋊C3×D61⋊C3, C3×#18011723⋊C2 |
| maximal quotient of | #28384434⋊C2, C3×#18011723⋊C2, #18011723⋊D3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 42);