Finite Group DatabasebetaFinite Group Databasebeta| order | 30124 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C443⋊#595 |
| Fitting, socle, derived, Hall | C17×C443 ⋊ C4 |
| Sylow | C443 ⋊ #595 |
| Sylow | C17 ⋊ Dic443 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C443 | C4 |
| prime radical, cosocle | D17×C443 | C2 |
| LCS | G ▷ C17×C443 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7531 |
Polycyclic presentation:
2^2,17,443|a^2=b,c^a=c^13,d^a=d^442,c^b=c^162218 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30124, 11);