Finite Group Databasebeta

D4×#13182039 #28379769

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD4×#13182039

Splittings

SylowC109 ⋊ D4×M16

Subgroups

subgroupG/H
center, FrattiniC22C23×#89137
commutator, socleC22×C109C23×C4
FittingC4×D4×C109C4
prime radicalC2×D4×D109C4
cosocleC2×Dic109C24
hypercenterC4×D4#89137
hypocenterC109D4×M16
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C4×D4

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

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, 21247);