Finite Group Databasebeta

#15784124

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28×C4

Aliases

No aliases for this group.

Splittings

FittingC13×C22⋊#95 ⋊ C2
SylowC13 ⋊ C4×#379

Subgroups

subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC13×C22⋊#95C2
socle, cosocleC24×C13C24
prime radicalC25×D13C22
hypercenterC22⋊#95D13
hypocenterC13C4×#379
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22⋊#95

6734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Polycyclic presentation:

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

Conjugacy classes & character table

448 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 90773);