Finite Group DatabasebetaFinite Group Databasebeta| order | 1274 |
| isoclinism | isoclinic class of C7⋊D91 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊D91 |
| unambiguous semidirect product | C13⋊(C7⋊D7) |
| Fitting, socle, derived, Hall | C72×C13 ⋊ C2 |
| Sylow | C72 ⋊ D13 |
| Sylow | C13 ⋊ C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C13 | C2 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 637 |
Polycyclic presentation:
2,7^2,13|b^a=b^6,c^a=c^6,d^a=d^12320 conjugacy classes — view the full character table.
| maximal subgroup of | D13×C7⋊D7, D7×D91, #14579330, … |
| maximal normal subgroup of | D13×C7⋊D7, D7×D91, #14579330, … |
| maximal quotient of | C7⋊Dic91, C2×C7⋊D91, C3×C7⋊D91, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1274, 9);