Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C52×C37 ⋊ C4×C9 |
| Hall | C52⋊#66524 ⋊ C4 |
| Hall | #16814879 ⋊ C9 |
| Sylow | C37 ⋊ #1043⋊C9 |
| Sylow | C52 ⋊ #13050607 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #26012840 |
| commutator, hypocenter | C52×C37 | C4×C9 |
| Fitting, socle | C3×C52×C37 | C3×C4 |
| prime radical, cosocle | C3×C37×C5⋊D5 | C2×C3 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1665 |
Polycyclic presentation:
2,3,2,5^2,37,3|a^2=c,b^3=g,d^a=d^3,e^a=e^3,f^a=f^36,d^b=de,e^b=d^2e^3,f^b=f^10,d^c=d^4,e^c=e^4294 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 242);