Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of D13⋊(C22⋊A4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D13⋊(C22⋊A4) |
| Fitting, socle, derived | C24×C13 ⋊ C2×C3 |
| Hall | C24×D13 ⋊ C3 |
| Sylow | C13 ⋊ C2×C22⋊A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C24×C13 | C2×C3 |
| LCS | G ▷ C24×C13 | |
| UCS | C1 | |
296 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
Polycyclic presentation:
2,3,2^4,13|g^a=g^12,c^b=cd,d^b=c,e^b=ef,f^b=e,g^b=g^348 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊A4×D13⋊C3, #72229136, #72242025, … |
| maximal normal subgroup of | C22⋊A4×D13⋊C3, #72229136, #72242025, … |
| maximal quotient of | #72229093 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1448);