Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C13 ⋊ #125 |
| Sylow | C13 ⋊ #889 |
| Sylow | C3 ⋊ #88143 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D39 |
| commutator, socle, prime radical, cosocle | C22×C3×C13 | C23 |
| Fitting | C3×C13×C4⋊C4 | C2 |
| hypercenter | C4⋊C4 | D39 |
| hypocenter | C3×C13 | #125 |
| LCS | G ▷ C22×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
112 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1248 |
Polycyclic presentation:
2^5,3,13|a^2=e,b^2=d,c^2=d,c^a=ce,f^a=f^2,g^a=g^12,c^b=cde204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1064);