Finite Group Databasebeta

C2×C22⋊#14270080 #28411442

order14656
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊#14270080

Splittings

SylowC229 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×D229
commutatorC2×C229C22×C8
FrattiniC2×C4C22×D229
FittingC23×C4×C229C2
socleC23×C229C2×C4
prime radicalC24×C229C4
cosocleC2×C4×C229C23
hypercenterC23×C4D229
hypocenterC229C2×C22⋊C8
LCSG ▷ C2×C229 ▷ C229
UCSC1 ◁ C22×C4 ◁ C23×C4

202 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, 510);