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C3×A4×3−1+2 #11758102

order972
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C2×C35

Aliases

direct productC3×A4×3−1+2

Splittings

FittingC22×C3×3−1+2 ⋊ C3
SylowC22 ⋊ C32×3−1+2

Subgroups

subgroupG/H
centerC32C32×A4
commutator, cosocleC22×C3C34
FrattiniC3C33×A4
FittingC22×C3×3−1+2C3
socleC22×C32C33
prime radicalC33×A4C3
hypercenterC3×3−1+2A4
hypocenterC22C32×3−1+2
LCSG ▷ C22×C3 ▷ C22
UCSC1 ◁ C32 ◁ C3×3−1+2

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×S4×3−1+2, 3−1+2×C3⋊S4, C3×A4⋊AGL(1,ℤ/9), …
maximal normal subgroup ofC3×S4×3−1+2, 3−1+2×C3⋊S4, C3×A4⋊AGL(1,ℤ/9), …
maximal quotient ofC3×SL(2,𝔽3)×3−1+2, C2×C3×A4×3−1+2, A4×#6891, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 827);