Finite Group DatabasebetaFinite Group Databasebeta| order | 31356 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| Fitting, socle, derived, Hall | C13×C67 ⋊ C22×C32 |
| Hall | C13⋊C3×C67⋊C3 ⋊ C22 |
| Hall | D13×D67 ⋊ C32 |
| Sylow | C67 ⋊ C2×C3×D13⋊C3 |
| Sylow | C13 ⋊ C2×C3×D67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C67 | C22×C32 |
| LCS | G ▷ C13×C67 | |
| UCS | C1 | |
120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 871 |
136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31356, 128);