Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52 · Schur multiplier (H2) = C2×C5 |
| Fitting, socle, derived, Hall | C22×C112 ⋊ C3×C52 |
| Hall | C22×C11⋊C52 ⋊ C3 |
| Hall | C112×A4 ⋊ C52 |
| Sylow | C112 ⋊ C52×A4 |
| Sylow | C22 ⋊ C3×C11⋊C52 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C112 | C3×C52 |
| LCS | G ▷ C22×C112 | |
| UCS | C1 | |
180 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 220 |
196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 473);