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 |
| Sylow | C112 ⋊ #1043⋊C3 |
| Sylow | C52 ⋊ #92150⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C112 | C3×C4 |
| prime radical | #31827692 | C2 |
| cosocle | C5⋊(C5⋊(C11⋊D11)) | C2×C3 |
| LCS | G ▷ C52×C112 | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 330 |
Polycyclic presentation:
2,3,2,5^2,11^2|a^2=c,d^a=d^2,e^a=e^2,f^a=f^3g^3,g^a=f^4g^8,d^b=de,e^b=d^2e^3,f^b=f^3g^9,g^b=fg^7,d^c=d^4,e^c=e^4,f^c=f^10,g^c=g^10264 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 707);