Finite Group DatabasebetaFinite Group Databasebeta| order | 7865 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#10597243 |
| Fitting, socle, Hall | C112×C13 ⋊ C5 |
| derived, Sylow | C112 ⋊ C5×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #10597243 |
| commutator, hypocenter | C112 | C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C112×C13 | C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C13 | |
56 conjugacy classes of subgroups.
377 conjugacy classes — view the full character table.
| maximal subgroup of | C13×#11925892, C13⋊#11925892, C13×#11925895, … |
| maximal normal subgroup of | C13×#11925892, C13⋊#11925892, C13×#11925895, … |
| maximal quotient of | C2×C13×#10597243, C3×C13×#10597243 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7865, 4);