Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C13 ⋊ #983 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | S4×D13 |
| commutator, cosocle, hypocenter | C13×SL(2,𝔽3) | C22 |
| Fitting | Q8×C13 | C2×D3 |
| socle | C2×C13 | C2×S4 |
| LCS | G ▷ C13×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 | |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^2,3,13,2^3|e^2=g,f^2=g,b^a=bg,d^a=d^12,c^b=c^2,e^b=ef,f^b=fg,e^c=f,f^c=efg,f^e=fg61 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1179);