Finite Group DatabasebetaFinite Group Databasebeta| order | 3477 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C19×C61 ⋊ C3 |
| Sylow | C61 ⋊ C19⋊C3 |
| Sylow | C19 ⋊ C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C61 | C3 |
| LCS | G ▷ C19×C61 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 80 |
| transitive degree | μt(G) = 1159 |
Polycyclic presentation:
3,19,61|b^a=b^7,c^a=c^13389 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊#16812464, C5×#16812464, #16812464⋊C5, … |
| maximal normal subgroup of | C5×#16812464, #16812464⋊C5, C7×#16812464, … |
| maximal quotient of | C22⋊#16812464, C5×#16812464, C7×#16812464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3477, 3);