Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C13×#2824 ⋊ C2 |
| Sylow | C13 ⋊ #36670 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D13 |
| commutator, socle, cosocle | C23×C13 | C25 |
| Fitting | C13×#2824 | C2 |
| hypercenter | #2824 | D13 |
| hypocenter | C13 | #36670 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #2824 | |
1794 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^8,13|a^2=g,b^2=g,e^2=f,b^a=bf,c^a=cg,d^a=dh,c^b=ch,d^c=dfh,i^e=i^12208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 375955);