Finite Group Databasebeta

#486×Dic43 #25104565

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct product#486×Dic43

Splittings

SylowC43 ⋊ C4×#486

Subgroups

subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#486C2
socleC23×C43C22×D4
prime radicalC2×#127×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#486D43
hypocenterC43C4×#486
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

1046 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 177536);