Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | D33⋊(C5⋊D55) |
| Fitting, socle, derived, Hall | C3×C52×C112 ⋊ C22 |
| Hall | C52×C112 ⋊ C2×D3 |
| Hall | C3×C112 ⋊ C2×C5⋊D5 |
| Sylow | C112 ⋊ D3×C5⋊D5 |
| Hall | C3×C52 ⋊ D112 |
| Sylow | C52 ⋊ D33⋊D11 |
| Sylow | C3 ⋊ D11×C5⋊D55 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C112 | C22 |
| LCS | G ▷ C3×C52×C112 | |
| UCS | C1 | |
480 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 85 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:
2^2,3,5^2,11^2|d^a=d^4,e^a=e^4,f^a=f^10,g^a=g^10,c^b=c^2,g^b=g^102487 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 933);