Finite Group Databasebeta

D4×#13093952 #26231953

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×#13093952

Splittings

FittingC42×D4×C47 ⋊ C2
SylowC47 ⋊ D4×#104

Subgroups

subgroupG/H
centerC2×C4C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC42×D4×C47C2
socleC22×C47C22×C22⋊C4
prime radicalD4×#10625350C2
cosocleC22×C4×C47C24
hypercenterC42×D4D47
hypocenterC47D4×#104
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ C42×D4

1608 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1910 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 185243);