Finite Group DatabasebetaFinite Group Databasebeta| order | 30212 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C83 · Schur multiplier (H2) = C1 |
| direct product | C83×C7⋊#261 |
| unambiguous semidirect product | C7⋊(#261×C83) |
| Fitting, socle, Hall | C7×C13×C83 ⋊ C4 |
| derived, Hall | C7×C13 ⋊ C4×C83 |
| Hall | C13×C83 ⋊ Dic7 |
| Hall | C7×C83 ⋊ #261 |
| Sylow | C13 ⋊ Dic7×C83 |
| Sylow | C7 ⋊ #261×C83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C83 | C7⋊#261 |
| commutator, hypocenter | C7×C13 | C4×C83 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C83 | C4 |
| prime radical | C7×D13×C83 | C2 |
| cosocle | C7×D13 | C2×C83 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C83 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7553 |
2573 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30212, 14);