Finite Group DatabasebetaFinite Group Databasebeta| order | 30926 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C47 |
| unambiguous semidirect product | C7⋊(C47⋊D47) |
| unambiguous semidirect product | C47⋊D329 |
| Fitting, socle, derived, Hall | C7×C472 ⋊ C2 |
| Sylow | C472 ⋊ D7 |
| Sylow | C7 ⋊ C47⋊D47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C472 | C2 |
| LCS | G ▷ C7×C472 | |
| UCS | C1 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15463 |
Polycyclic presentation:
2,7,47^2|b^a=b^6,c^a=c^46,d^a=d^467733 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30926, 10);