Finite Group Databasebeta

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H(3,𝔽3)×#11758603 #41008573

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

Aliases

direct productH(3,𝔽3)×#11758603

Splittings

SylowC37 ⋊ C27×H(3,𝔽3)

Subgroups

subgroupG/H
center, FrattiniC32C32×#66526
commutatorC3×C37C32×C27
Fitting, prime radicalC3×H(3,𝔽3)×C37C9
socleC32×C37C32×C9
cosocleC3×#66524C33
hypercenterC3×H(3,𝔽3)#66526
hypocenterC37C27×H(3,𝔽3)
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C32 ◁ C3×H(3,𝔽3)

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8991

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 4344);