Finite Group Databasebeta

D4×#13093934 #26214737

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26

Aliases

direct productD4×#13093934

Splittings

SylowC47 ⋊ D4×#97

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D47
commutatorC22×C47C22×C42
FittingC2×C8×D4×C47C2
socleC23×C47C23×C4
prime radicalC22×D4×C47C2×C4
cosocleC22×C4×C47C24
hypercenterC2×C8×D4D47
hypocenterC47D4×#97
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C8×D4

1274 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 168027);