Finite Group DatabasebetaFinite Group Databasebeta| order | 30212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C13 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×C13×D83 |
| unambiguous semidirect product | C83⋊(C22×C7×C13) |
| unambiguous semidirect product | (C2×C83)⋊(C2×C7×C13) |
| Fitting, socle | C2×C7×C13×C83 ⋊ C2 |
| derived, Sylow | C83 ⋊ C22×C7×C13 |
| Hall | C7×C13×C83 ⋊ C22 |
| Hall | C13×C83 ⋊ C22×C7 |
| Hall | C7×C83 ⋊ C22×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7×C13 | D83 |
| commutator, cosocle, hypocenter | C83 | C22×C7×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C13×C83 | C2 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C2×C7×C13 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15106 |
7826 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30212, 21);