Finite Group Databasebeta

D16×D223 #28383999

order14272
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productD16×D223

Splittings

FittingD16×C223 ⋊ C2
SylowC223 ⋊ C2×D16

Subgroups

subgroupG/H
centerC2D8×D223
commutator, cosocleC8×C223C23
FrattiniC8C22×D223
FittingD16×C223C2
socleC2×C223C2×D8
hypercenterD16D223
hypocenterC223C2×D16
LCSG ▷ C8×C223 ▷ C4×C223 ▷ C2×C223 ▷ C223
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D16

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3568

Conjugacy classes & character table

1243 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14272, 968);