Finite Group Databasebeta

#509×Dic43 #25249917

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

Aliases

direct product#509×Dic43

Splittings

SylowC43 ⋊ C4×#509

Subgroups

subgroupG/H
centerC22C2×D8×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
Fitting, prime radicalC2×C43×#509C2
socleC22×C43C22×D8
cosocleC2×C8×C43C24
hypercenterC2×#509D43
hypocenterC43C4×#509
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

738 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, 322888);