Finite Group Databasebeta

C4×#16814676 #28412443

order14656
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#16814676

Splittings

SylowC229 ⋊ C4×M16

Subgroups

subgroupG/H
centerC2×C4C2×#11745021
commutatorC2×C229C2×C42
FrattiniC22C22×#11745021
FittingC42×C229C4
socleC22×C229C22×C4
prime radicalC22×D229C2×C4
cosocleC2×Dic229C23
hypercenterC42#11745021
hypocenterC229C4×M16
LCSG ▷ C2×C229 ▷ C229
UCSC1 ◁ C2×C4 ◁ C42

142 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, 1511);