Finite Group Databasebeta

#15750730

order3328
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #7513

Subgroups

subgroupG/H
centerC16C22⋊Dic13
commutatorC22×C13C2×C32
FrattiniC2×C32C2×D13
FittingC2×C13×M64C2
socleC2×C13C22⋊C32
prime radicalC23×C13C32
cosocleC2×C13×C32C22
hypercenterC2×M64D13
hypocenterC13#7513
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C16 ◁ C2×C32 ◁ C2×M64

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Polycyclic presentation:

2^8,13|a^2=d,d^2=e,e^2=f,f^2=g,g^2=h,b^a=bc,c^a=ch,i^a=i^12,d^b=dh

Conjugacy classes & character table

568 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 57379);