Finite Group Databasebeta

Q32×C22⋊D43 #25253321

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productQ32×C22⋊D43

Splittings

FittingC22×Q32×C43 ⋊ C2
SylowC43 ⋊ D4×Q32

Subgroups

subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC22×Q32×C43C2
socleC22×C43C22×D8
prime radicalC2×C22⋊D43D8
hypercenterC22×Q32D43
hypocenterC43D4×Q32
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q32

664 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

979 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 326292);