Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| direct product | D41×C3⋊((C5⋊D5)⋊C3) |
| unambiguous semidirect product | (C3×D41)⋊((C5⋊D5)⋊C3) |
| unambiguous semidirect product | (D41×C3⋊(C5⋊D5))⋊C3 |
| Fitting, socle, derived | C3×C52×C41 ⋊ C22×C3 |
| Hall | C3×C41×C52⋊C3 ⋊ C22 |
| Hall | C52×C41 ⋊ C2×C3×D3 |
| Hall | C3×C52⋊C3 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×C3⋊((C5⋊D5)⋊C3) |
| Sylow | C52 ⋊ C3×D3×D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C41 | C22×C3 |
| LCS | G ▷ C3×C52×C41 | |
| UCS | C1 | |
128 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1845 |
462 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 416);