Finite Group Databasebeta

C2×#20294865 #28365334

order13952
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#20294865

Splittings

FittingC2×C32×C109 ⋊ C2
SylowC109 ⋊ C2×SD64

Subgroups

subgroupG/H
centerC22D1744
commutator, cosocleC16×C109C23
FrattiniC16C22×D109
FittingC2×C32×C109C2
socleC22×C109D16
prime radicalC2×D1744C2
hypercenterC2×C32D109
hypocenterC109C2×SD64
LCSG ▷ C16×C109 ▷ C8×C109 ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

3494 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 6812);