Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#1009 |
| Fitting | C3×C13×#41 ⋊ C2 |
| Hall | C3×C13 ⋊ H(5,𝔽2) |
| Sylow | C3 ⋊ C13×H(5,𝔽2) |
332 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 312 |
A minimal faithful permutation representation — 4 generators on 24 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16)(17,19,20,23)(18,22,21,24);(18,21)(22,24);(17,18)(19,22)(20,21)(23,24);(15,16)(19,23)(22,24)351 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1408);