Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Fitting, socle, derived, Hall | C52×C37 ⋊ C4×C9 |
| Hall | C52⋊#66526 ⋊ C4 |
| Hall | #16814887 ⋊ C9 |
| Sylow | C37 ⋊ #1039⋊C9 |
| Sylow | C52 ⋊ AGL(1,𝔽37) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C37 | C4×C9 |
| prime radical, cosocle | C52×D37⋊C3 | C2×C3 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 555 |
Polycyclic presentation:
2,3,2,3,5^2,37|a^2=c,b^3=d,e^a=e^4,f^a=f^4,g^a=g^31,e^b=ef^3,f^b=e^4f^3,g^b=g^16,g^c=g^36,g^d=g^2685 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 417);