Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×C4×C13 ⋊ C2×C4 |
| Hall | C3×C13 ⋊ C4×D4 |
| Sylow | C13 ⋊ #893 |
| Sylow | C3 ⋊ D4×#261 |
188 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 156 |
Polycyclic presentation:
2^5,3,13|a^2=d,c^2=e,c^a=ce,g^a=g^8,c^b=ce,f^b=f^2,g^d=g^1257 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D4×#261, #72241925, #72241926 |
| maximal normal subgroup of | D3×D4×#261, #72241925 |
| maximal quotient of | #72241926 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1204);