Finite Group Databasebeta

#15785147

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #13904

Subgroups

subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C22⋊C4C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×C4×C22⋊C4D13
hypocenterC13#13904
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

2278 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Polycyclic presentation:

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

Conjugacy classes & character table

556 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 91796);