Finite Group DatabasebetaFinite Group Databasebeta| order | 3354 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C43 ⋊ C2×C3 |
| Hall | #13131976 ⋊ C2 |
| Hall | C13×D43 ⋊ C3 |
| Hall | D43 ⋊ C13⋊C3 |
| Sylow | C43 ⋊ C2×C13⋊C3 |
| Sylow | C13 ⋊ D43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C43 | C2×C3 |
| LCS | G ▷ C13×C43 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 56 |
| transitive degree | μt(G) = 559 |
Polycyclic presentation:
2,3,13,43|d^a=d^42,c^b=c^3,d^b=d^36105 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#16809809, C5⋊#16809809, C7×#16809809, … |
| maximal normal subgroup of | C5×#16809809, C7×#16809809, #16809809⋊C7, … |
| maximal quotient of | C5×#16809809, C5⋊#16809809, C7×#16809809, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3354, 15);