Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D605⋊D15 |
| Fitting, derived, Hall | C3×C52×C121 ⋊ C22 |
| Hall | C52×C121 ⋊ C2×D3 |
| Hall | C3×C121 ⋊ D52 |
| Sylow | C121 ⋊ D5×D15 |
| Hall | C3×C52 ⋊ C2×D121 |
| Sylow | C52 ⋊ D3×D121 |
| Sylow | C3 ⋊ (C5⋊D5)⋊D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C52×C121 | C22 |
| Frattini | C11 | D55⋊D15 |
| socle | C3×C52×C11 | C2×D11 |
| LCS | G ▷ C3×C52×C121 | |
| UCS | C1 | |
144 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3630 |
Polycyclic presentation:
2^2,3,5^2,11^2|f^11=g^10,d^a=d^4,f^a=f^10g,g^a=g^10,c^b=c^2,d^b=d^4,e^b=e^42376 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 135);