Finite Group Databasebeta

C32⋊C9×#66524 #41005091

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

Aliases

direct productC32⋊C9×#66524

Splittings

SylowC37 ⋊ C9×C32⋊C9

Subgroups

subgroupG/H
center, FrattiniC33C32×C37⋊C3
commutatorC3×C37C3×C92
FittingC3×C37×C32⋊C9C3
socle, cosocleC33×C37C33
prime radicalC34×C37C32
hypercenterC3×C32⋊C9C37⋊C3
hypocenterC37C9×C32⋊C9
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C33 ◁ C3×C32⋊C9

662 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 238 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) = 8991

Conjugacy classes & character table

1485 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 862);