Finite Group DatabasebetaFinite Group Databasebeta| order | 1350 |
| isoclinism | isoclinic class of #13062498 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Fitting, derived | C52×C9 ⋊ C2×C3 |
| Hall | C9×C52⋊C3 ⋊ C2 |
| Sylow | C52 ⋊ C3×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C52×C9 | C2×C3 |
| Frattini | C3 | C3⋊((C5⋊D5)⋊C3) |
| socle | C3×C52 | C3×D3 |
| LCS | G ▷ C52×C9 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
Polycyclic presentation:
2,3^2,5^2,3|c^3=f,c^a=c^2f^2,d^a=d^4,e^a=e^4,f^a=f^2,d^b=de,e^b=d^2e^354 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1350, 57);