Finite Group Databasebeta

D4×#13182006 #28365849

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

Aliases

direct productD4×#13182006

Splittings

FittingC2×C4×D4×C109 ⋊ C2
SylowC109 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D109
commutatorC22×C109C23×C4
FittingC2×C4×D4×C109C2
socle, cosocleC23×C109C24
prime radicalC22×D4×D109C2
hypercenterC2×C4×D4D109
hypocenterC109D4×C22⋊C4
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ C2×C4×D4

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

2210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 7327);