Finite Group Databasebeta

D4×#13093938 #26231597

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD4×#13093938

Splittings

FittingD4×C22⋊C4×C47 ⋊ C2
SylowC47 ⋊ D4×#99

Subgroups

subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingD4×C22⋊C4×C47C2
socleC22×C47C22×C22⋊C4
prime radicalC2×D4×C22⋊D47C2
cosocleC24×C47C24
hypercenterD4×C22⋊C4D47
hypocenterC47D4×#99
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×D4 ◁ D4×C22⋊C4

2102 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1205 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 184887);