Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×C13⋊#11925890 |
| unambiguous semidirect product | (C2×C13)⋊#11925890 |
| Fitting, socle | C2×C112×C13 ⋊ D5 |
| derived, Hall | C13×#10597245 ⋊ C22 |
| Hall | C112×C13 ⋊ C2×D5 |
| Hall | #10597245 ⋊ C2×D13 |
| Sylow | C112 ⋊ C2×D65 |
| Sylow | C13 ⋊ C2×#11925890 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C13⋊#11925890 |
| commutator, cosocle, hypocenter | C13×#10597245 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C112×C13 | D5 |
| LCS | G ▷ C13×#10597245 | |
| UCS | C1 ◁ C2 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 572 |
410 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 140);