Finite Group Databasebeta

#15750814

order3328
automorphism?
homologyAbelianization (H1) = C2×C64 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ C4⋊C64

Subgroups

subgroupG/H
center, FrattiniC2×C32C2×D13
commutatorC2×C13C2×C64
FittingC2×C13×C64C2
socle, prime radicalC22×C13C2×C32
cosocleC2×C13×C32C22
hypercenterC2×C64D13
hypocenterC13C4⋊C64
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C32 ◁ C2×C64

74 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Polycyclic presentation:

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

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 57463);