Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of C22⋊(C22⋊(C13⋊C3)) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊(C22⋊(C13⋊C3)) |
| unambiguous semidirect product | (C2×C13)⋊(C22⋊A4) |
| Fitting, socle, Hall | C25×C13 ⋊ C3 |
| derived | C24×C13 ⋊ C2×C3 |
| Sylow | C25 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ C2×C22⋊A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C22⋊(C22⋊(C13⋊C3)) |
| commutator, cosocle, hypocenter | C24×C13 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C25×C13 | C3 |
| LCS | G ▷ C24×C13 | |
| UCS | C1 ◁ C2 | |
296 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1456);