Finite Group DatabasebetaFinite Group Databasebeta| order | 30212 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C83⋊#261) |
| unambiguous semidirect product | C83⋊(C7⋊#261) |
| Fitting, socle, derived, Hall | C7×C13×C83 ⋊ C4 |
| Hall | C13×C83 ⋊ Dic7 |
| Hall | C7×C83 ⋊ #261 |
| Hall | C7×C13 ⋊ Dic83 |
| Sylow | C83 ⋊ C7⋊#261 |
| Sylow | C13 ⋊ Dic581 |
| Sylow | C7 ⋊ C83⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C13×C83 | C4 |
| prime radical, cosocle | C7×D13×C83 | C2 |
| LCS | G ▷ C7×C13×C83 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7553 |
Polycyclic presentation:
2^2,7,13,83|a^2=b,c^a=c^6,d^a=d^5,e^a=e^82,d^b=d^122327 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30212, 15);