Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C13 ⋊ A4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | S4×D13 |
| commutator, prime radical, cosocle | C2×A4×C13 | C22 |
| Fitting, socle | C23×C13 | C2×D3 |
| hypocenter | A4×C13 | Q8 |
| LCS | G ▷ C2×A4×C13 ▷ A4×C13 | |
| UCS | C1 ◁ C2 | |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 312 |
Polycyclic presentation:
2^3,3,13,2^2|a^2=c,b^2=c,b^a=bc,e^a=e^12,d^b=d^2,f^b=fg,f^d=g,g^d=fg74 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1182);