Finite Group DatabasebetaFinite Group Databasebeta| order | 32450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊((C11⋊C5)⋊D59) |
| unambiguous semidirect product | (C11⋊C5)⋊D295 |
| unambiguous semidirect product | C59⋊(C5⋊AGL(1,𝔽11)) |
| unambiguous semidirect product | D3245⋊C5 |
| Fitting, socle, derived | C5×C11×C59 ⋊ C2×C5 |
| Hall | C5×C11⋊C5×C59 ⋊ C2 |
| Hall | C11×C59 ⋊ C5×D5 |
| Hall | C5×C11⋊C5 ⋊ D59 |
| Sylow | C59 ⋊ C5⋊AGL(1,𝔽11) |
| Sylow | C11 ⋊ C5×D295 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C11×C59 | C2×C5 |
| LCS | G ▷ C5×C11×C59 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3245 |
Polycyclic presentation:
2,5^2,11,59|c^a=c^4,d^a=d^10,e^a=e^58,d^b=d^41040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32450, 18);