Finite Group Databasebeta

D4×#88238 #16808326

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD4×#88238

Splittings

SylowC13 ⋊ D4×#131

Subgroups

subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingD42×C13C4
prime radicalD4×#6129C2
cosocleC2×Dic13C25
hypercenterD42#261
hypocenterC13D4×#131
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ D42

2814 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114975);