Finite Group Databasebeta

C2×#20294859 #28365323

order13952
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productC2×#20294859

Splittings

FittingC2×C32×C109 ⋊ C2
SylowC109 ⋊ C2×M64

Subgroups

subgroupG/H
centerC2×C16C2×D109
commutatorC2×C109C22×C16
FrattiniC16C22×D109
FittingC2×C32×C109C2
socleC22×C109C2×C16
prime radicalC22×D109C16
cosocleC16×C109C23
hypercenterC2×C32D109
hypocenterC109C2×M64
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C16 ◁ C2×C32

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

3536 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 6801);