Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C13 ⋊ D16 |
| Sylow | C13 ⋊ #826 |
| Sylow | C3 ⋊ D208 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #10597596 |
| commutator, Fitting, cosocle | C3×C8×C13 | C22 |
| Frattini, hypercenter | C8 | D3×D13 |
| socle | C2×C3×C13 | D8 |
| hypocenter | C3×C13 | D16 |
| LCS | G ▷ C3×C8×C13 ▷ C3×C4×C13 ▷ C2×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 624 |
Polycyclic presentation:
2^5,3,13|b^2=cd,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,g^a=g^12,f^b=f^2162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 58);