Finite Group Databasebeta

C9×C32⋊#66526 #41008436

order26973
automorphism?
homologyAbelianization (H1) = C3×C92 · Schur multiplier (H2) = C33×C9

Aliases

direct productC9×C32⋊#66526

Splittings

FittingC32×C9×C37 ⋊ C9
SylowC37 ⋊ C9×C32⋊C9

Subgroups

subgroupG/H
centerC3×C9C3×#66526
commutatorC3×C37C3×C92
FrattiniC32C32×#66526
FittingC32×C9×C37C9
socleC32×C37C32×C9
prime radicalC33×C37⋊C3C32
cosocleC32×C37⋊C3C33
hypercenterC32×C9#66526
hypocenterC37C9×C32⋊C9
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C3×C9 ◁ C32×C9

662 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degreeμt(G) = 2997

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 4207);