Finite Group DatabasebetaFinite Group Databasebeta| order | 2756 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C53 · Schur multiplier (H2) = C2 |
| direct product | C2×D13×C53 |
| unambiguous semidirect product | C13⋊(C22×C53) |
| unambiguous semidirect product | (C2×C13)⋊(C2×C53) |
| Fitting, socle | C2×C13×C53 ⋊ C2 |
| derived, Sylow | C13 ⋊ C22×C53 |
| Hall | C13×C53 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C53 | D13 |
| commutator, cosocle, hypocenter | C13 | C22×C53 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C53 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C53 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1378 |
848 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D13×C53, C2×C53×D65, C2×C5×D13×C53, … |
| maximal normal subgroup of | C2×C5×D13×C53, C2×C7×D13×C53, C2×C11×D13×C53, … |
| maximal quotient of | D5×D13×C53, C2×C53×D65, C2×C5×D13×C53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2756, 19);