Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×C11×C11⋊#3874 |
| unambiguous semidirect product | (C2×C11)⋊(C11×#3874) |
| Fitting, socle | C2×C52×C112 ⋊ D3 |
| derived | C11×C52⋊C3 ⋊ C22×C11 |
| Hall | C112×C52⋊C3 ⋊ C22 |
| Hall | C52×C112 ⋊ C2×D3 |
| Sylow | C112 ⋊ C2×#3874 |
| Hall | C52⋊C3 ⋊ C2×C11×D11 |
| Sylow | C52 ⋊ C2×C11×D33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | C11⋊#3874 |
| commutator, cosocle, hypocenter | C11×C52⋊C3 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C112 | D3 |
| LCS | G ▷ C11×C52⋊C3 | |
| UCS | C1 ◁ C2×C11 | |
180 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 660 |
1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 823);