Finite Group DatabasebetaFinite Group Databasebeta| order | 3350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D335 |
| unambiguous semidirect product | C67⋊(C5⋊D5) |
| Fitting, socle, derived, Hall | C52×C67 ⋊ C2 |
| Sylow | C67 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C67 | C2 |
| LCS | G ▷ C52×C67 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1675 |
Polycyclic presentation:
2,5^2,67|b^a=b^4,c^a=c^4,d^a=d^66839 conjugacy classes — view the full character table.
| maximal subgroup of | C7×C5⋊D335, C5⋊D2345, C5⋊(C5⋊(D67⋊C11)), … |
| maximal normal subgroup of | C7×C5⋊D335, C5⋊(C5⋊(D67⋊C11)), C11×C5⋊D335 |
| maximal quotient of | C7×C5⋊D335, C5⋊D2345, C11×C5⋊D335, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3350, 10);