Finite Group DatabasebetaFinite Group Databasebeta| order | 1350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊(C5⋊#272) |
| Fitting, derived, Hall | C52×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C5⋊D5 |
| Sylow | C52 ⋊ #272 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C3⋊(C3⋊(C5⋊D5)) |
| commutator, Fitting, cosocle, hypocenter | C52×H(3,𝔽3) | C2 |
| socle | C3×C52 | C3⋊D3 |
| LCS | G ▷ C52×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 225 |
Polycyclic presentation:
2,3^2,5^2,3|b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^4,c^b=cf142 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1350, 88);