Finite Group DatabasebetaFinite Group Databasebeta| order | 1281 |
| isoclinism | isoclinic class of #13046197 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C61 ⋊ C3 |
| Sylow | C61 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C61 | C3 |
| LCS | G ▷ C7×C61 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 68 |
| transitive degree | μt(G) = 427 |
Polycyclic presentation:
3,7,61|b^a=b^4,c^a=c^13145 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13046197, #14579420, #14579424, … |
| maximal normal subgroup of | C2×#13046197, #14579420, #14579424, … |
| maximal quotient of | C2×#13046197, #16838636, C3×#13046197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1281, 4);