Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C5 |
No aliases for this group.
| derived, Hall | C52×C37 ⋊ C4×C9 |
| Hall | C52×#66526 ⋊ C4 |
| Hall | #16814867 ⋊ C9 |
| Hall | #66526 ⋊ #1039 |
| Sylow | C37 ⋊ C9×#1039 |
| Sylow | C52 ⋊ #13050625 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(C5⋊(#66526⋊C2)) |
| commutator, hypocenter | C52×C37 | C4×C9 |
| Fitting, socle | C2×C52×C37 | C2×C9 |
| prime radical, cosocle | C2×C52×C37⋊C3 | C2×C3 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 ◁ C2 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3700 |
Polycyclic presentation:
2,3^2,5^2,37,2|a^2=g,b^3=c,d^a=d^4,e^a=e^4,f^a=f^36,f^b=f^16,f^c=f^26352 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 350);