Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Sylow | C13 ⋊ #62624 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C24×D13 |
| commutator, socle | C2×C13 | C24×C8 |
| Fitting | C13×#3573 | C2 |
| prime radical | C13×#585 | C4 |
| cosocle | C8×C13 | C25 |
| hypercenter | #3573 | D13 |
| hypocenter | C13 | #62624 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C8 ◁ #3573 | |
2038 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^8,13|a^2=f,f^2=g,g^2=h,i^a=i^12,e^b=eh,d^c=dh544 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1076039);