Finite Group Databasebeta

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C2×C3×C3⋊#4174 #72244465

order2916
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32

Aliases

direct productC2×C3×C3⋊#4174

Splittings

FittingC2×C32×AΣL(1,𝔽27) ⋊ C2
derivedC3×H(3,𝔽3) ⋊ C22×C32
SylowC32×AΣL(1,𝔽27) ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C32C3⋊((C3⋊D3)⋊C3)
commutator, cosocle, hypocenterC3×H(3,𝔽3)C22×C32
FrattiniC32C2×C32×C3⋊D3
FittingC2×C32×AΣL(1,𝔽27)C2
socleC2×C33(C3⋊D3)⋊C3
LCSG ▷ C3×H(3,𝔽3)
UCSC1 ◁ C2×C32

2216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72221865, C2×C3×#13091105, C2×#72221880, …
maximal normal subgroup ofC2×#72221880, C2×#72221894

GAP

Past the SmallGroups library coverage — no SmallGroups id.