Finite Group Databasebeta

D32×D109 #28365328

order13952
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productD32×D109

Splittings

FittingD32×C109 ⋊ C2
SylowC109 ⋊ C2×D32

Subgroups

subgroupG/H
centerC2D16×D109
commutator, cosocleC16×C109C23
FrattiniC16C22×D109
FittingD32×C109C2
socleC2×C109C2×D16
hypercenterD32D109
hypocenterC109C2×D32
LCSG ▷ C16×C109 ▷ C8×C109 ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D32

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 6806);