Finite Group Databasebeta

D4×#14556517 #33101652

order18688
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×#14556517

Splittings

FittingD4×M16×C73 ⋊ C2
SylowC73 ⋊ D4×#104

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingD4×M16×C73C2
socleC22×C73C22×C22⋊C4
prime radicalD4×#11924028C2
cosocleC22×C4×C73C24
hypercenterD4×M16D73
hypocenterC73D4×#104
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×M16

1608 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

Conjugacy classes & character table

1870 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 185236);