Finite Group Databasebeta

C22×#16814654 #28412254

order14656
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×#16814654

Splittings

SylowC229 ⋊ C22×SD16

Subgroups

subgroupG/H
centerC23C22⋊D229
commutator, cosocleC4×C229C24
FrattiniC4C23×D229
Fitting, prime radicalC22×D4×C229C2
socleC23×C229D4
hypercenterC22×D4D229
hypocenterC229C22×SD16
LCSG ▷ C4×C229 ▷ C2×C229 ▷ C229
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7328

Conjugacy classes & character table

2308 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 1322);