Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C13×#564 ⋊ C4 |
| Sylow | C13 ⋊ #34530 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×#261 |
| commutator, socle | C22×C13 | C24×C4 |
| Fitting | C13×#564 | C4 |
| prime radical, cosocle | C22×D13 | C25 |
| hypercenter | #564 | #261 |
| hypocenter | C13 | #34530 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #564 | |
1800 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^8,13|a^2=h,b^2=g,c^2=fh,d^2=g,e^2=h,b^a=bf,c^a=cg,d^a=dg,e^a=ef,i^a=i^5,c^b=cg,d^b=df,i^c=i^5,i^e=i^8,i^h=i^12133 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1114641);