Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| direct product | C3×#27130929 |
| Fitting, socle | C3×C5×C112 ⋊ C2×D5 |
| derived, Hall | C5×#10597245 ⋊ C22×C3 |
| Hall | C3×C5×#10597245 ⋊ C22 |
| Hall | C3×C112 ⋊ C2×C5⋊D5 |
| Sylow | C112 ⋊ C2×C3×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #27130929 |
| commutator, cosocle, hypocenter | C5×#10597245 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C112 | C2×D5 |
| LCS | G ▷ C5×#10597245 | |
| UCS | C1 ◁ C3 | |
232 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 330 |
219 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 529);