Finite Group Databasebeta

C22×#16814676 #28412555

order14656
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22×#16814676

Splittings

SylowC229 ⋊ C22×M16

Subgroups

subgroupG/H
centerC23C2×#11745021
commutatorC2×C229C23×C4
FrattiniC2C23×#11745021
FittingC22×C4×C229C4
socleC23×C229C2×C4
prime radicalC23×D229C4
cosocleDic229C24
hypercenterC22×C4#11745021
hypocenterC229C22×M16
LCSG ▷ C2×C229 ▷ C229
UCSC1 ◁ C23 ◁ C22×C4

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 1623);