Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C13 ⋊ C4⋊C8 |
| Sylow | C13 ⋊ Dic3⋊C8 |
| Sylow | C3 ⋊ #88112 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D3×#261 |
| commutator | C2×C3×C13 | C2×C8 |
| Fitting, socle, prime radical | C22×C3×C13 | C2×C4 |
| cosocle | C2×C3×Dic13 | C22 |
| hypocenter | C3×C13 | C4⋊C8 |
| LCS | G ▷ C2×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C22 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1248 |
Polycyclic presentation:
2^5,3,13|a^2=c,b^2=de,c^2=e,b^a=bd,g^a=g^8,f^b=f^2,g^c=g^1272 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 336);