Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Hall | C52×C112 ⋊ Dic3 |
| derived, Hall | C52×C112⋊C3 ⋊ C4 |
| Hall | C112⋊C3 ⋊ #1043 |
| Sylow | C112 ⋊ C3⋊#1043 |
| Sylow | C52 ⋊ #13089712 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C52×C112⋊C3 | C4 |
| Fitting, socle | C52×C112 | Dic3 |
| prime radical, cosocle | C5⋊D5×C112⋊C3 | C2 |
| LCS | G ▷ C52×C112⋊C3 | |
| UCS | C1 | |
160 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 825 |
Polycyclic presentation:
2^2,3,5^2,11^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^2,f^a=fg^4,g^a=g^10,d^b=d^4,e^b=e^4,f^c=f^2g^10,g^c=f^7g^8334 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 753);