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C3×H(3,𝔽3)×C31⋊C9 #36382251

order22599
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C37

Aliases

direct productC3×H(3,𝔽3)×C31⋊C9

Splittings

SylowC31 ⋊ C3×C9×H(3,𝔽3)

Subgroups

subgroupG/H
centerC33C32×C31⋊C3
commutatorC3×C31C33×C9
FrattiniC32C33×C31⋊C3
Fitting, prime radicalC32×H(3,𝔽3)×C31C3
socleC33×C31C33
cosocleC32×C31C34
hypercenterC32×H(3,𝔽3)C31⋊C3
hypocenterC31C3×C9×H(3,𝔽3)
LCSG ▷ C3×C31 ▷ C31
UCSC1 ◁ C33 ◁ C32×H(3,𝔽3)

1688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7533

Conjugacy classes & character table

1287 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22599, 3272);