Finite Group DatabasebetaFinite Group Databasebeta| order | 1378 |
| isoclinism | isoclinic class of C53⋊C13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C2×C53⋊C13 |
| unambiguous semidirect product | (C2×C53)⋊C13 |
| Fitting, socle, Hall | C2×C53 ⋊ C13 |
| derived, Sylow | C53 ⋊ C2×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C53⋊C13 |
| commutator, cosocle, hypocenter | C53 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C53 | C13 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 106 |
34 conjugacy classes — view the full character table.
| maximal subgroup of | Dic53⋊C13, C4×C53⋊C13, C2×D53⋊C13, … |
| maximal normal subgroup of | Dic53⋊C13, C4×C53⋊C13, C2×D53⋊C13, … |
| maximal quotient of | C4×C53⋊C13, C22×C53⋊C13, C2×C3×C53⋊C13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1378, 2);