Finite Group DatabasebetaFinite Group Databasebeta| order | 31228 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D37×D211 |
| unambiguous semidirect product | (D37×C211)⋊C2 |
| unambiguous semidirect product | (C37×D211)⋊C2 |
| unambiguous semidirect product | D7807⋊C2 |
| Fitting, socle, derived, Hall | C37×C211 ⋊ C22 |
| Sylow | C211 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×D211 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C37×C211 | C22 |
| LCS | G ▷ C37×C211 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7807 |
2140 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31228, 8);