Finite Group Databasebeta

C32×#15688502 #41007487

order26973
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C37

Aliases

direct productC32×#15688502

Splittings

FittingC33×C9×C37 ⋊ C3
SylowC37 ⋊ C32×C32⋊C9

Subgroups

subgroupG/H
centerC34C3×C37⋊C3
commutatorC3×C37C33×C9
FrattiniC32C33×C37⋊C3
FittingC33×C9×C37C3
socleC34×C37C32
prime radicalC34×C37⋊C3C3
cosocleC32×C37C34
hypercenterC33×C9C37⋊C3
hypocenterC37C32×C32⋊C9
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C34 ◁ C33×C9

2996 conjugacy classes of subgroups; only the 814 normal subgroups are shown.

normal subgroups only

This group has 2996 conjugacy classes of subgroups — too many to draw. Only its 814 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

3213 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 3258);