Finite Group Databasebeta

D4×#13093989 #26376139

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD4×#13093989

Splittings

SylowC47 ⋊ C4×D4×Q8

Subgroups

subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingD4×C4⋊C4×C47C2
socle, cosocleC23×C47C25
prime radicalC22×D4×C47C23
hypercenterD4×C4⋊C4D47
hypocenterC47C4×D4×Q8
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ D4×C4⋊C4

3148 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 329429);