Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #23372 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×#261 |
| commutator, socle, prime radical | C23×C13 | C23×C4 |
| Fitting | C13×#382 | C4 |
| cosocle | C22×Dic13 | C24 |
| hypercenter | #382 | #261 |
| hypocenter | C13 | #23372 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #382 | |
584 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 194 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3328 |
Polycyclic presentation:
2^8,13|a^2=g,b^2=f,c^2=f,d^2=e,g^2=h,b^a=be,c^a=cf,d^a=defh,i^a=i^8,c^b=cefh,d^b=deh,i^b=i^12,i^d=i^12,i^g=i^12136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1113292);