Finite Group Databasebeta

C2×#20300927 #28411895

order14656
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#20300927

Splittings

FittingC2×C16×C229 ⋊ C2
SylowC229 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×D229
commutatorC2×C229C22×C8
FrattiniC8C22×D229
FittingC2×C16×C229C2
socleC22×C229C2×C8
prime radicalC22×D229C8
cosocleC8×C229C23
hypercenterC2×C16D229
hypocenterC229C2×M32
LCSG ▷ C2×C229 ▷ C229
UCSC1 ◁ C2×C8 ◁ C2×C16

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7328

Conjugacy classes & character table

3688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 963);