Finite Group DatabasebetaFinite Group Databasebeta| order | 13790 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C197 · Schur multiplier (H2) = C1 |
| direct product | C7×D5×C197 |
| unambiguous semidirect product | C5⋊(C2×C7×C197) |
| Fitting, socle, Hall | C5×C7×C197 ⋊ C2 |
| derived, Sylow | C5 ⋊ C2×C7×C197 |
| Hall | C5×C197 ⋊ C2×C7 |
| Hall | C5×C7 ⋊ C2×C197 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C197 | D5 |
| commutator, cosocle, hypocenter | C5 | C2×C7×C197 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C197 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C7×C197 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6895 |
5516 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×AGL(1,𝔽5)×C197, C7×#16841101, C7⋊AGL(1,𝔽5)×C197, … |
| maximal normal subgroup of | C7×AGL(1,𝔽5)×C197, C7×#16841101, C7⋊AGL(1,𝔽5)×C197, … |
| maximal quotient of | C7×Dic5×C197, C2×C7×D5×C197 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13790, 6);