Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
No aliases for this group.
| derived, Hall | C52×C112⋊C3 ⋊ C4 |
| Hall | C52×C112 ⋊ Dic3 |
| Hall | C112⋊C3 ⋊ #1039 |
| Sylow | C112 ⋊ C3⋊#1039 |
| Sylow | C52 ⋊ #13089712 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(C5⋊#10624391) |
| commutator, hypocenter | C52×C112⋊C3 | C4 |
| Fitting, socle | C2×C52×C112 | D3 |
| prime radical, cosocle | C2×C52×C112⋊C3 | C2 |
| LCS | G ▷ C52×C112⋊C3 | |
| UCS | C1 ◁ C2 | |
160 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3300 |
Polycyclic presentation:
2,3,5^2,11^2,2|a^2=g,b^a=b^2,c^a=c^4,d^a=d^4,f^a=e^4f^10,e^b=e^7f^10,f^b=e^2f^31108 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 422);