Finite Group DatabasebetaFinite Group Databasebeta| order | 30044 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16864281⋊C7 |
| Fitting, socle, derived, Hall | C29×C37 ⋊ C4×C7 |
| Hall | C37×C29⋊C7 ⋊ C4 |
| Hall | #16864281 ⋊ C7 |
| Hall | C29⋊C7 ⋊ #3866 |
| Sylow | C37 ⋊ AGL(1,𝔽29) |
| Sylow | C29 ⋊ C7×#3866 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C29×C37 | C4×C7 |
| prime radical | C37⋊(D29⋊C7) | C2 |
| cosocle | D1073 | C2×C7 |
| LCS | G ▷ C29×C37 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1073 |
Polycyclic presentation:
2,7,2,29,37|a^2=c,d^a=d^17,e^a=e^6,d^b=d^16,d^c=d^28,e^c=e^36128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30044, 16);