Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊(C11⋊#64470) |
| derived, Hall | C112×C52⋊C3 ⋊ C4 |
| Hall | C52×C112 ⋊ Dic3 |
| Sylow | C112 ⋊ #64470 |
| Hall | C52⋊C3 ⋊ C11⋊Dic11 |
| Sylow | C52 ⋊ C3⋊(C11⋊Dic11) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊(C11⋊#3874) |
| commutator, hypocenter | C112×C52⋊C3 | C4 |
| Fitting, socle | C2×C52×C112 | D3 |
| prime radical, cosocle | C2×C112×C52⋊C3 | C2 |
| LCS | G ▷ C112×C52⋊C3 | |
| UCS | C1 ◁ C2 | |
252 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7260 |
Polycyclic presentation:
2,3,11^2,5^2,2|a^2=g,b^a=b^2,c^a=c^10,d^a=d^10,e^a=e^2f,f^a=e^2f^3,e^b=e^2f^4,f^b=e^2f^21346 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 427);