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AΣL(1,𝔽27)×C31⋊C3 #21419373

order7533
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C33

Aliases

direct productAΣL(1,𝔽27)×C31⋊C3

Splittings

FittingC31×AΣL(1,𝔽27) ⋊ C3
SylowC31 ⋊ C3×AΣL(1,𝔽27)

Subgroups

subgroupG/H
centerC3H(3,𝔽3)×C31⋊C3
commutatorC32×C31C33
FrattiniC32C32×C31⋊C3
FittingC31×AΣL(1,𝔽27)C3
socleC3×C31C3×H(3,𝔽3)
hypercenterAΣL(1,𝔽27)C31⋊C3
hypocenterC31C3×AΣL(1,𝔽27)
LCSG ▷ C32×C31 ▷ C3×C31 ▷ C31
UCSC1 ◁ C3 ◁ C32 ◁ AΣL(1,𝔽27)

252 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

221 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AΣL(1,𝔽27)×C31⋊C3, C31⋊C3×#6908, C31⋊C3×#6909, …
maximal normal subgroup ofC3×AΣL(1,𝔽27)×C31⋊C3, C31⋊C3×#6908, C31⋊C3×#6909, …
maximal quotient ofC31⋊C3×#6856, C31⋊C3×#6857, C31⋊C3×#6858, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7533, 243);