Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of D13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C210 |
| direct product | C24×D13⋊C3 |
| unambiguous semidirect product | D13⋊(C24×C3) |
| unambiguous semidirect product | (C13⋊C3)⋊C25 |
| unambiguous semidirect product | (C2×C13⋊C3)⋊C24 |
| Fitting, socle | C24×C13 ⋊ C2×C3 |
| derived, Sylow | C13 ⋊ C25×C3 |
| Hall | C24×D13 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C25×C3 |
| Frattini | C1 | G |
| Fitting, socle | C24×C13 | C2×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C24 | |
1496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #120×D13⋊C3, C24×AGL(1,𝔽13), #72228996, … |
| maximal normal subgroup of | #120×D13⋊C3, C24×AGL(1,𝔽13), #72228996, … |
| maximal quotient of | H(5,𝔽2)×D13⋊C3, C23×#11759815⋊C2, C2×#41×D13⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1444);