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C32×#15688518 #41008136

order26973
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C37

Aliases

direct productC32×#15688518

Splittings

FittingC32×H(3,𝔽3)×C37 ⋊ C3
SylowC37 ⋊ C32×#732

Subgroups

subgroupG/H
centerC33C32⋊(C37⋊C3)
commutator, cosocleC32×C37C34
FrattiniC32C33×C37⋊C3
FittingC32×H(3,𝔽3)×C37C3
socleC33×C37H(3,𝔽3)
hypercenterC32×H(3,𝔽3)C37⋊C3
hypocenterC37C32×#732
LCSG ▷ C32×C37 ▷ C3×C37 ▷ C37
UCSC1 ◁ C33 ◁ C34 ◁ C32×H(3,𝔽3)

1376 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8991

Conjugacy classes & character table

1341 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 3907);