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C37⋊C3×C32⋊H(3,𝔽3) #41007530

order26973
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C39

Aliases

direct productC37⋊C3×C32⋊H(3,𝔽3)

Splittings

FittingC37×C32⋊H(3,𝔽3) ⋊ C3
SylowC37 ⋊ C3×C32⋊H(3,𝔽3)

Subgroups

subgroupG/H
center, FrattiniC32C33×C37⋊C3
commutator, socle, cosocleC32×C37C34
FittingC37×C32⋊H(3,𝔽3)C3
hypercenterC32⋊H(3,𝔽3)C37⋊C3
hypocenterC37C3×C32⋊H(3,𝔽3)
LCSG ▷ C32×C37 ▷ C37
UCSC1 ◁ C32 ◁ C32⋊H(3,𝔽3)

3824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 999

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 3301);