Finite Group Databasebeta

C2×M32×D109 #28376126

order13952
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×M32×D109

Splittings

FittingC2×M32×C109 ⋊ C2
SylowC109 ⋊ C22×M32

Subgroups

subgroupG/H
centerC2×C8C22×D109
commutatorC2×C109C23×C8
FrattiniC8C23×D109
FittingC2×M32×C109C2
socleC22×C109C22×C8
prime radicalC23×D109C8
cosocleC8×C109C24
hypercenterC2×M32D109
hypocenterC109C22×M32
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C8 ◁ C2×M32

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

2240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 17604);