Finite Group Databasebeta

D4×#88077 #15878593

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

Aliases

direct productD4×#88077

Splittings

SylowC13 ⋊ D4×#104

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalD4×C13×#41C2
socleC22×C13C22×C22⋊C4
cosocleC22×C4×C13C24
hypercenterD4×#41D13
hypocenterC13D4×#104
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×#41

1608 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 185242);