Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C11 |
| unambiguous semidirect product | ((C5⋊D5)⋊C3)⋊(C11⋊D11) |
| Fitting, socle, Hall | C52×C112 ⋊ C2×D3 |
| derived, Hall | C112×C52⋊C3 ⋊ C22 |
| Sylow | C112 ⋊ #3874⋊C2 |
| Hall | C52⋊C3 ⋊ C2×C11⋊D11 |
| Sylow | C52 ⋊ C2×C3⋊(C11⋊D11) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C112×C52⋊C3 | C22 |
| Fitting, socle | C52×C112 | C2×D3 |
| LCS | G ▷ C112×C52⋊C3 | |
| UCS | C1 | |
420 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1815 |
Polycyclic presentation:
2^2,3,11^2,5^2|c^a=c^2,d^a=d^10,e^a=e^10,f^a=f^4g^4,f^b=f^4,g^b=g^4,f^c=g,g^c=f^4g^4614 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 719);