Finite Group DatabasebetaFinite Group Databasebeta| order | 728 |
| isoclinism | isoclinic class of D7×D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | D7×Dic13 |
| derived, Hall | C7×C13 ⋊ C2×C4 |
| Sylow | C13 ⋊ C4×D7 |
| Sylow | C7 ⋊ C2×Dic13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7×D13 |
| commutator, hypocenter | C7×C13 | C2×C4 |
| Fitting, socle, cosocle | C2×C7×C13 | C22 |
| prime radical | C2×C13×D7 | C2 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 364 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1057, #13089839, D7×Dic26, … |
| maximal normal subgroup of | D7×#1057, #13089839, D7×Dic26, … |
| maximal quotient of | D7×#1055, #13089757, Dic7×Dic13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(728, 8);