Finite Group Databasebeta

#16769538

order3328
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #62652

Subgroups

subgroupG/H
center, FrattiniC22C25×D13
commutatorC2×C13C25×C4
Fitting, prime radicalC22×C13×H(5,𝔽2)C2
socle, cosocleC22×C13C26
hypercenterC22×H(5,𝔽2)D13
hypocenterC13#62652
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×H(5,𝔽2)

11674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Polycyclic presentation:

2^8,13|a^2=h,b^a=bg,f^a=fg,i^a=i^12,e^b=eg,d^c=dg

Conjugacy classes & character table

538 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076187);