Finite Group DatabasebetaFinite Group Databasebeta| order | 31072 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×Dic971 |
| unambiguous semidirect product | (C2×C971)⋊C42 |
| derived, Sylow | C971 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D971 |
| commutator, hypocenter | C971 | C2×C42 |
| Frattini | C22 | C22×D971 |
| Fitting | C22×C4×C971 | C2 |
| socle, prime radical | C23×C971 | C22 |
| cosocle | C22×C971 | C23 |
| LCS | G ▷ C971 | |
| UCS | C1 ◁ C22×C4 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31072 |
7792 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31072, 95);