Finite Group Databasebeta

D4×C22⋊#89137 #28379534

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD4×C22⋊#89137

Splittings

FittingC22×D4×C109 ⋊ C4
SylowC109 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C23×#89137
commutator, socleC22×C109C23×C4
FittingC22×D4×C109C4
prime radicalC22×D4×D109C2
cosocleC22×D109C24
hypercenterC22×D4#89137
hypocenterC109D4×C22⋊C4
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×D4

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1744

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 21012);