Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Sylow | C13 ⋊ #15143 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D13 |
| commutator, socle, prime radical, cosocle | C24×C13 | C24 |
| Fitting | C22×C13×C4⋊Q8 | C2 |
| hypercenter | C22×C4⋊Q8 | D13 |
| hypocenter | C13 | #15143 |
| LCS | G ▷ C24×C13 ▷ C13 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊Q8 | |
1934 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3328 |
Polycyclic presentation:
2^8,13|a^2=e,b^2=e,c^2=f,d^2=h,b^a=be,c^a=cf,d^a=dh,c^b=cg,i^c=i^12400 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 106277);