Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | ((C11⋊C5)⋊D11)⋊D15 |
| Fitting, socle, derived | C3×C5×C112 ⋊ C22×C5 |
| Hall | C3×C5×C11×C11⋊C5 ⋊ C22 |
| Hall | C5×C11×C11⋊C5 ⋊ C2×D3 |
| Hall | C3×C112 ⋊ C2×C5×D5 |
| Sylow | C112 ⋊ C2×C5×D15 |
| Sylow | C3 ⋊ (C5⋊AGL(1,𝔽11))⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C112 | C22×C5 |
| LCS | G ▷ C3×C5×C112 | |
| UCS | C1 | |
200 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1650 |
Polycyclic presentation:
2^2,5,3,5,11^2|d^a=d^2,e^a=e^4,f^a=f^10,f^b=f^10,g^b=g^10,g^c=g^4399 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 601);