Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C42 |
No aliases for this group.
| Sylow | C13 ⋊ #14663 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D13 |
| commutator | C23×C13 | C23×C4 |
| Fitting | C13×#1445 | C2 |
| socle, prime radical, cosocle | C24×C13 | C24 |
| hypercenter | #1445 | D13 |
| hypocenter | C13 | #14663 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C24 ◁ #1445 | |
1462 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3328 |
Polycyclic presentation:
2^8,13|a^2=f,b^2=h,c^2=e,d^2=e,b^a=be,c^a=cf,c^b=cg,d^b=def,d^c=de,i^d=i^12316 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 100613);