Finite Group Databasebeta

#15752282

order3328
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C22×C4

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #7842

Subgroups

subgroupG/H
center, FrattiniC2×C42C22×D13
commutatorC22×C13C43
FittingC13×#1744C2
socle, prime radicalC23×C13C2×C42
cosocleC2×C42×C13C23
hypercenter#1744D13
hypocenterC13#7842
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ #1744

558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Polycyclic presentation:

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

Conjugacy classes & character table

592 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 58931);