Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#10597792 |
| Fitting | C2×C3×D4×C13 ⋊ C2 |
| Hall | C3×C13 ⋊ C2×#41 |
| Sylow | C13 ⋊ C2×#237 |
| Sylow | C3 ⋊ C2×#6129 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D39 |
| commutator, cosocle | C2×C3×C13 | C24 |
| Frattini | C2 | C23×D39 |
| Fitting | C2×C3×D4×C13 | C2 |
| socle | C22×C3×C13 | C23 |
| hypercenter | C2×D4 | D39 |
| hypocenter | C3×C13 | C2×#41 |
| LCS | G ▷ C2×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
328 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 624 |
210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1417);