Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
No aliases for this group.
| Fitting, socle, derived, Hall | C52×C112 ⋊ C3×C4 |
| Hall | #27130977 ⋊ C3 |
| Hall | C52×C112⋊C3 ⋊ C4 |
| Hall | C112⋊C3 ⋊ #1043 |
| Sylow | C112 ⋊ C3×#1043 |
| Sylow | C52 ⋊ #92150⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C112 | C3×C4 |
| prime radical | C5⋊(C5⋊((C11⋊D11)⋊C3)) | C2 |
| cosocle | C5⋊(C5⋊(C11⋊D11)) | C2×C3 |
| LCS | G ▷ C52×C112 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1650 |
Polycyclic presentation:
2,3,2,5^2,11^2|a^2=c,d^a=d^2,e^a=e^2,f^a=f^5g^7,g^a=fg^6,f^b=f^9g^10,g^b=f^3g,d^c=d^4,e^c=e^4,f^c=f^10,g^c=g^10280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 756);