Finite Group DatabasebetaFinite Group Databasebeta| order | 9516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×#18011727 |
| Fitting, socle | C2×C13×C61 ⋊ C2×C3 |
| derived, Hall | C13×C61 ⋊ C22×C3 |
| Hall | C2×D13×C61 ⋊ C3 |
| Hall | #14558652 ⋊ C22 |
| Sylow | C61 ⋊ C2×D13⋊C3 |
| Hall | C2×D13 ⋊ C61⋊C3 |
| Sylow | C13 ⋊ C22×C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #18011727 |
| commutator, cosocle, hypocenter | C13×C61 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C61 | C2×C3 |
| LCS | G ▷ C13×C61 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
336 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D13⋊C3×C61⋊C3, D3×#18011727, C2×C3×#18011727, … |
| maximal normal subgroup of | C2×D13⋊C3×C61⋊C3, C2×C3×#18011727 |
| maximal quotient of | C2×#28384438, D3×#18011727, C2×C3×#18011727, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 59);