Finite Group Databasebeta

C3×C32⋊#11758603 #41008477

order26973
automorphism?
homologyAbelianization (H1) = C32×C27 · Schur multiplier (H2) = C34

Aliases

direct productC3×C32⋊#11758603

Splittings

SylowC37 ⋊ C3×C32⋊C27

Subgroups

subgroupG/H
centerC33C3×#66526
commutatorC3×C37C32×C27
FrattiniC32C32×#66526
Fitting, prime radicalC34×C37C9
socleC33×C37C3×C9
cosocleC3×#66524C33
hypercenterC34#66526
hypocenterC37C3×C32⋊C27
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C33 ◁ C34

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8991

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, 4248);