Finite Group Databasebeta

D4×#13093951 #26231952

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

Aliases

direct productD4×#13093951

Splittings

SylowC47 ⋊ D4×#104

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalD4×#41×C47C2
socleC22×C47C22×C22⋊C4
cosocleC22×C4×C47C24
hypercenterD4×#41D47
hypocenterC47D4×#104
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×#41

1608 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 185242);