Finite Group Databasebeta

#15780531

order3328
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C2×C4

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #13104

Subgroups

subgroupG/H
center, FrattiniC22×C8C22×D13
commutatorC22×C13C22×C16
FittingC2×C13×C4⋊C16C2
socle, prime radicalC23×C13C22×C8
cosocleC22×C8×C13C23
hypercenterC2×C4⋊C16D13
hypocenterC13#13104
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C2×C4⋊C16

326 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Polycyclic presentation:

2^8,13|a^2=f,b^2=f,c^2=d,f^2=g,g^2=h,b^a=bd,c^a=ce,i^c=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, 87180);