Finite Group Databasebeta

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C3×H(3,𝔽3)×#66524 #41007501

order26973
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C37

Aliases

direct productC3×H(3,𝔽3)×#66524

Splittings

SylowC37 ⋊ C3×C9×H(3,𝔽3)

Subgroups

subgroupG/H
centerC33C32×C37⋊C3
commutatorC3×C37C33×C9
FrattiniC32C33×C37⋊C3
Fitting, prime radicalC32×H(3,𝔽3)×C37C3
socleC33×C37C33
cosocleC32×C37C34
hypercenterC32×H(3,𝔽3)C37⋊C3
hypocenterC37C3×C9×H(3,𝔽3)
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C33 ◁ C32×H(3,𝔽3)

1688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8991

Conjugacy classes & character table

1485 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 3272);