Finite Group DatabasebetaFinite Group Databasebeta| order | 30212 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C83 · Schur multiplier (H2) = C1 |
| direct product | C83×Dic91 |
| unambiguous semidirect product | C7⋊(Dic13×C83) |
| derived, Hall | C7×C13 ⋊ C4×C83 |
| Hall | C7×C13×C83 ⋊ C4 |
| Hall | C13×C83 ⋊ Dic7 |
| Hall | C7×C83 ⋊ Dic13 |
| Sylow | C13 ⋊ Dic7×C83 |
| Sylow | C7 ⋊ Dic13×C83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C83 | D91 |
| commutator, hypocenter | C7×C13 | C4×C83 |
| Frattini | C2 | C83×D91 |
| Fitting, socle, prime radical | C2×C7×C13×C83 | C2 |
| cosocle | C2×C7×C13 | C2×C83 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C2×C83 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30212 |
7802 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30212, 7);