Finite Group DatabasebetaFinite Group Databasebeta| order | 13952 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C109 ⋊ #2396 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D109 |
| commutator, socle, cosocle | C23×C109 | C24 |
| Fitting | #393×C109 | C2 |
| prime radical | C24×C109 | C23 |
| hypercenter | #393 | D109 |
| hypocenter | C109 | #2396 |
| LCS | G ▷ C23×C109 ▷ C109 | |
| UCS | C1 ◁ C23 ◁ #393 | |
528 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 6976 |
Polycyclic presentation:
2^7,109|a^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^d=h^1081232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13952, 7777);