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3−1+2×C22⋊C9 #11757842

order972
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C2×C32

Aliases

direct product3−1+2×C22⋊C9

Splittings

SylowC22 ⋊ C9×3−1+2

Subgroups

subgroupG/H
center, FrattiniC32C32×A4
commutatorC22×C3C32×C9
FittingC22×C3×3−1+2C3
socle, cosocleC22×C32C33
prime radicalC22×C33C32
hypercenterC3×3−1+2A4
hypocenterC22C9×3−1+2
LCSG ▷ C22×C3 ▷ C22
UCSC1 ◁ C32 ◁ C3×3−1+2

186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 162

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup of3−1+2×(C22⋊C9)⋊C2, #14518080, C22⋊C9×AGL(1,ℤ/9), …
maximal normal subgroup of3−1+2×(C22⋊C9)⋊C2, #14518080, C22⋊C9×AGL(1,ℤ/9), …
maximal quotient of3−1+2×Q8⋊C9, C2×3−1+2×C22⋊C9, C22⋊C9×#1094

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 567);