Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (#11925890⋊C5)⋊D3 |
| unambiguous semidirect product | (#11925890⋊D3)⋊C5 |
| Fitting, socle, Hall | C3×C112 ⋊ C2×C5×D5 |
| derived | C3×#10597245 ⋊ C22×C5 |
| Hall | C3×C11⋊C52 ⋊ C22 |
| Hall | C11⋊C52 ⋊ C2×D3 |
| Sylow | C112 ⋊ C5×D3×D5 |
| Sylow | C3 ⋊ (#11925890⋊C2)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×#10597245 | C22×C5 |
| Fitting, socle | C3×C112 | C2×C5×D5 |
| LCS | G ▷ C3×#10597245 | |
| UCS | C1 | |
168 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 66 |
Polycyclic presentation:
2^2,5,3,5,11^2|d^a=d^2,e^a=e^4,f^a=f^4g^2,g^a=f^9g^7,e^b=e^4,f^b=f^7g^9,g^b=f^2g^4,f^c=f^9,g^c=g^9,f^e=f^3g^9,g^e=g^484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 467);