Finite Group Databasebeta

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C3×#14578895 #21419376

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

Aliases

direct productC3×#14578895

Splittings

FittingC3×3−1+2×C31 ⋊ C3
SylowC31 ⋊ C3×AΣL(1,𝔽27)

Subgroups

subgroupG/H
centerC32C32⋊(C31⋊C3)
commutatorC32×C31C33
FrattiniC32C32×C31⋊C3
FittingC3×3−1+2×C31C3
socleC32×C31H(3,𝔽3)
hypercenterC3×3−1+2C31⋊C3
hypocenterC31C3×AΣL(1,𝔽27)
LCSG ▷ C32×C31 ▷ C3×C31 ▷ C31
UCSC1 ◁ C32 ◁ C33 ◁ C3×3−1+2

252 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

381 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#36381121, C9×#14578895, #36381146, …
maximal normal subgroup of#36381121, C9×#14578895, #36381146, …
maximal quotient ofC3×#21419201, C3×#21419202, C3×#21419204, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7533, 246);