Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊#16814855) |
| Fitting, derived, Hall | C32×C25×C37 ⋊ C4 |
| Hall | C25×C37 ⋊ C3⋊Dic3 |
| Hall | C32×C37 ⋊ #1035 |
| Hall | C32×C25 ⋊ #3866 |
| Sylow | C37 ⋊ C3⋊(C3⋊#1035) |
| Sylow | C25 ⋊ C3⋊(C3⋊#3866) |
| Sylow | C32 ⋊ #16814855 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C32×C25×C37 | C4 |
| Frattini | C5 | C3⋊(C3⋊#10625192) |
| socle | C32×C5×C37 | AGL(1,𝔽5) |
| prime radical, cosocle | C32×D925 | C2 |
| LCS | G ▷ C32×C25×C37 | |
| UCS | C1 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8325 |
Polycyclic presentation:
2^2,3^2,5,37,5|a^2=b,e^5=g,c^a=c^2,d^a=d^2,e^a=e^2g,f^a=f^6,g^a=g^2,e^b=e^4g^4,f^b=f^36,g^b=g^42091 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 168);