Finite Group Databasebeta

C32⋊C9×#66526 #41008437

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

Aliases

direct productC32⋊C9×#66526

Splittings

FittingC37×C32⋊C9 ⋊ C9
SylowC37 ⋊ C9×C32⋊C9

Subgroups

subgroupG/H
center, FrattiniC32C32×#66526
commutatorC3×C37C3×C92
FittingC37×C32⋊C9C9
socleC32×C37C32×C9
prime radicalC33×C37⋊C3C32
cosocleC32×C37⋊C3C33
hypercenterC32⋊C9#66526
hypocenterC37C9×C32⋊C9
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C32 ◁ C32⋊C9

662 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 180 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) = 999

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 4208);