Finite Group Databasebeta

D4×C43⋊C32 #25017144

order11008
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C23

Aliases

direct productD4×C43⋊C32

Splittings

SylowC43 ⋊ D4×C32

Subgroups

subgroupG/H
center, FrattiniC2×C16C22×D43
commutatorC2×C43C22×C32
FittingD4×C16×C43C2
socleC22×C43C22×C16
prime radicalC2×D4×C43C16
cosocleC2×C16×C43C23
hypercenterD4×C16D43
hypocenterC43D4×C32
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C16 ◁ D4×C16

214 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 90115);