Finite Group Databasebeta

D4×#14581718 #35420072

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×#14581718

Splittings

FittingD4×M16×C83 ⋊ C2
SylowC83 ⋊ D4×#104

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingD4×M16×C83C2
socleC22×C83C22×C22⋊C4
prime radicalD4×#13050590C2
cosocleC22×C4×C83C24
hypercenterD4×M16D83
hypocenterC83D4×#104
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×M16

1608 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

Conjugacy classes & character table

2120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 185236);