Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×C42×C13 ⋊ C2 |
| Hall | C3×C13 ⋊ #127 |
| Sylow | C13 ⋊ #874 |
| Sylow | C3 ⋊ #88128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D39 |
| commutator, socle, cosocle | C22×C3×C13 | C23 |
| Fitting | C3×C42×C13 | C2 |
| hypercenter | C42 | D39 |
| hypocenter | C3×C13 | #127 |
| LCS | G ▷ C22×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C22 ◁ C42 | |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 624 |
Polycyclic presentation:
2^5,3,13|b^2=e,c^2=d,b^a=be,c^a=cd,f^a=f^2,g^a=g^12318 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1048);