Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C5 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C52×C37 ⋊ C4 |
| Hall | C52×C37 ⋊ #157 |
| Hall | C32×C37 ⋊ #1044 |
| Hall | C32×C52 ⋊ #3866 |
| Sylow | C37 ⋊ #11744708 |
| Sylow | C52 ⋊ #13050652 |
| Sylow | C32 ⋊ #16814881 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C52×C37 | C4 |
| prime radical, cosocle | C3⋊(C3⋊(C5⋊D185)) | C2 |
| LCS | G ▷ C32×C52×C37 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1110 |
Polycyclic presentation:
2^2,3^2,5^2,37|a^2=b,c^a=cd,d^a=cd^2,e^a=e^2,f^a=f^3,g^a=g^31,c^b=c^2,d^b=d^2,e^b=e^4,f^b=f^4,g^b=g^362085 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 654);