Finite Group DatabasebetaFinite Group Databasebeta| order | 29150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(C53⋊AGL(1,𝔽11)) |
| unambiguous semidirect product | C53⋊(C5⋊AGL(1,𝔽11)) |
| unambiguous semidirect product | (C11⋊C5)⋊D265 |
| unambiguous semidirect product | D2915⋊C5 |
| Fitting, socle, derived | C5×C11×C53 ⋊ C2×C5 |
| Hall | C5×C53×C11⋊C5 ⋊ C2 |
| Hall | C11×C53 ⋊ C5×D5 |
| Hall | C5×C11⋊C5 ⋊ D53 |
| Sylow | C53 ⋊ C5⋊AGL(1,𝔽11) |
| Sylow | C11 ⋊ C5×D265 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C11×C53 | C2×C5 |
| LCS | G ▷ C5×C11×C53 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2915 |
Polycyclic presentation:
2,5^2,11,53|c^a=c^4,d^a=d^10,e^a=e^52,d^b=d^4935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29150, 18);