Finite Group DatabasebetaFinite Group Databasebeta| order | 1456 |
| isoclinism | isoclinic class of D7×D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | Dic7×Dic13 |
| derived, Hall | C7×C13 ⋊ C42 |
| Sylow | C13 ⋊ C4×Dic7 |
| Sylow | C7 ⋊ C4×Dic13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D7×D13 |
| commutator, hypocenter | C7×C13 | C42 |
| Fitting, socle, prime radical, cosocle | C22×C7×C13 | C22 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C22 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1456 |
160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1456, 25);