Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×((C5⋊D5)⋊C3)⋊D17 |
| unambiguous semidirect product | ((C5⋊D5)⋊C3)⋊(C3×D17) |
| Fitting, socle | C3×C52×C17 ⋊ C2×D3 |
| derived | C17×C52⋊C3 ⋊ C22×C3 |
| Hall | C3×C17×C52⋊C3 ⋊ C22 |
| Hall | C52×C17 ⋊ C2×C3×D3 |
| Hall | C3×C52⋊C3 ⋊ C2×D17 |
| Sylow | C52 ⋊ C2×C3×D51 |
| Sylow | C17 ⋊ C3×#3874⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | ((C5⋊D5)⋊C3)⋊D17 |
| commutator, cosocle, hypocenter | C17×C52⋊C3 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C17 | C2×D3 |
| LCS | G ▷ C17×C52⋊C3 | |
| UCS | C1 ◁ C3 | |
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) = 765 |
282 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 258);