Finite Group Databasebeta

D43×#1366 #25007959

order11008
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productD43×#1366

Splittings

FittingC43×#1366 ⋊ C2
SylowC43 ⋊ C2×#1366

Subgroups

subgroupG/H
centerC2#333×D43
commutatorC42×C43C22×C4
FrattiniC4×C8C22×D43
FittingC43×#1366C2
socleC2×C43C2×#333
prime radicalC22×D43#100
cosocleC4×C8×C43C23
hypercenter#1366D43
hypocenterC43C2×#1366
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1366

294 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 91 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

529 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 80930);