Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×#6131 |
| Fitting | C3×Q8×C13 ⋊ C22 |
| Hall | C3×C13 ⋊ C2×#41 |
| Sylow | C13 ⋊ D3×#41 |
| Sylow | C3 ⋊ C2×#6131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D3×D13 |
| commutator, socle, cosocle | C2×C3×C13 | C24 |
| Fitting | C3×Q8×C13 | C22 |
| hypercenter | Q8 | D3×D13 |
| hypocenter | C3×C13 | C2×#41 |
| LCS | G ▷ C2×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
328 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 312 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1341);