Finite Group Databasebeta

D4×#14270087 #28412507

order14656
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productD4×#14270087

Splittings

SylowC229 ⋊ C8×D4

Subgroups

subgroupG/H
center, FrattiniC22C22×#11745021
commutatorC2×C229C22×C8
Fitting, prime radicalC2×D4×C229C4
socleC22×C229C22×C4
cosocleC2×Dic229C23
hypercenterC2×D4#11745021
hypocenterC229C8×D4
LCSG ▷ C2×C229 ▷ C229
UCSC1 ◁ C22 ◁ C2×D4

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 1575);