Finite Group Databasebeta

#472×Dic43 #25103478

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#472×Dic43

Splittings

SylowC43 ⋊ C4×#472

Subgroups

subgroupG/H
centerC22#121×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#472C2
socleC22×C43C2×#121
cosocleC22×C4×C43C24
hypercenterC2×#472D43
hypocenterC43C4×#472
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#472

946 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 176449);