Finite Group Databasebeta

#15793679

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C2×C43

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #14632

Subgroups

subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#394C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC2×#394D13
hypocenterC13#14632
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#394

1586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Polycyclic presentation:

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

Conjugacy classes & character table

316 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 100328);