Finite Group Databasebeta

#15784642

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #13846

Subgroups

subgroupG/H
centerC23×C4C22×D13
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC2×C13×#376C2
socle, prime radical, cosocleC24×C13C24
hypercenterC2×#376D13
hypocenterC13#13846
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C2×#376

1422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Polycyclic presentation:

2^8,13|a^2=h,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,i^c=i^12

Conjugacy classes & character table

568 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 91291);