Finite Group Databasebeta

C9×C27×C37⋊C3 #41006189

order26973
automorphism?
homologyAbelianization (H1) = C3×C9×C27 · Schur multiplier (H2) = C32×C9

Aliases

direct productC9×C27×C37⋊C3

Splittings

FittingC9×C27×C37 ⋊ C3
derived, SylowC37 ⋊ C3×C9×C27

Subgroups

subgroupG/H
center, hypercenterC9×C27C37⋊C3
commutator, hypocenterC37C3×C9×C27
FrattiniC3×C9C32×C37⋊C3
FittingC9×C27×C37C3
socleC32×C37C32×C9
prime radicalC32×C37⋊C3C3×C9
cosocleC3×C9×C37C33
LCSG ▷ C37
UCSC1 ◁ C9×C27

404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8991

Conjugacy classes & character table

3645 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 1960);