Finite Group Databasebeta

C22×D13⋊#131 #16809647

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

Aliases

direct productC22×D13⋊#131
unambiguous semidirect productD13⋊(C22×#131)

Splittings

SylowC13 ⋊ C23×#131

Subgroups

subgroupG/H
centerC22×C4C22×#261
commutatorC2×C13C25×C4
FrattiniC2C25×#261
FittingC22×C13×#41C4
socleC23×C13C23×C4
prime radicalC22×#41×D13C2
cosocleDic13C26
hypercenterC22×#41#261
hypocenterC13C23×#131
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×#41

11422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

280 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1116296);