Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| Fitting, socle, derived, Hall | C3×C112 ⋊ C22×C52 |
| Hall | C3×C11⋊C52 ⋊ C22 |
| Hall | C11⋊C52 ⋊ C2×D3 |
| Hall | D33⋊D11 ⋊ C52 |
| Sylow | C112 ⋊ C2×C52×D3 |
| Sylow | C3 ⋊ AGL(1,𝔽11)2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C112 | C22×C52 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 | |
328 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 330 |
Polycyclic presentation:
2^2,5^2,3,11^2|e^a=e^2,f^a=f^10,f^b=f^10,g^b=g^10,f^c=f^4,f^d=f^4,g^d=g^4183 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 472);