Finite Group Databasebeta

#432×Dic43 #25094762

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct product#432×Dic43

Splittings

SylowC43 ⋊ C4×#432

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D43
commutatorC22×C43C22×C42
FittingC2×C43×#432C2
socleC23×C43C23×C4
prime radicalC24×C43C22×C4
cosocleC22×C4×C43C24
hypercenterC2×#432D43
hypocenterC43C4×#432
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#432

1206 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 167733);