Finite Group Databasebeta

C22×#14582744 #25254766

order11008
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C42

Aliases

direct productC22×#14582744

Splittings

SylowC43 ⋊ C22×#376

Subgroups

subgroupG/H
centerC25C22×D43
commutatorC2×C43C23×C42
FrattiniC23C24×D43
FittingC22×#95×C43C2
socle, prime radicalC25×C43C23
cosocleC23×C43C25
hypercenterC22×#95D43
hypocenterC43C22×#376
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C25 ◁ C22×#95

5150 conjugacy classes of subgroups; only the 2363 normal subgroups are shown.

normal subgroups only

This group has 5150 conjugacy classes of subgroups — too many to draw. Only its 2363 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, 327737);