Finite Group Databasebeta

D4×#88118 #16803086

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×#88118

Splittings

FittingD4×Q8×C13 ⋊ C4
SylowC13 ⋊ D4×#104

Subgroups

subgroupG/H
centerC22C22×C22⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingD4×Q8×C13C4
socleC22×C13C22×C22⋊C4
prime radicalD4×#6131C2
cosocleC2×C4×D13C24
hypercenterD4×Q8#261
hypocenterC13D4×#104
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

1608 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

145 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1109735);