Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×#11925890⋊C5 |
| unambiguous semidirect product | (C2×#11925890)⋊(C3×C5) |
| unambiguous semidirect product | (C2×C3×#11925890)⋊C5 |
| Fitting, socle | C2×C3×C112 ⋊ C5×D5 |
| derived | #10597245 ⋊ C22×C3×C5 |
| Hall | C3×C11⋊C52 ⋊ C22 |
| Hall | C11⋊C52 ⋊ C22×C3 |
| Hall | C3×C112 ⋊ C2×C5×D5 |
| Sylow | C112 ⋊ C2×C3×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #11925890⋊C5 |
| commutator, cosocle, hypocenter | #10597245 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C112 | C5×D5 |
| LCS | G ▷ #10597245 | |
| UCS | C1 ◁ C2×C3 | |
168 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 132 |
210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 488);