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(C₁₅₁⋊C₉)⋊C₉ #27133545

order	12231
automorphism	?
homology	Abelianization (H₁) = C₃×C₉ · Schur multiplier (H₂) = C₃

Aliases

unambiguous semidirect product

(C₁₅₁⋊C₉)⋊C₉

Splittings

C₁₅₁ ⋊ C₉⋊C₉

Subgroups

	subgroup	G/H
center, Frattini	C₃²	C₃×C₁₅₁⋊C₃
commutator	C₃×C₁₅₁	C₃×C₉
Fitting	C₃×C₉×C₁₅₁	C₃
socle, prime radical, cosocle	C₃²×C₁₅₁	C₃²
hypercenter	C₃×C₉	C₁₅₁⋊C₃
hypocenter	C₁₅₁	C₉⋊C₉
LCS	G ▷ C₃×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₃² ◁ C₃×C₉

34 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

3^4,151|a^3=d,b^3=c,b^a=bc,e^b=e^32

Conjugacy classes & character table

1383 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉⋊C₉×C₁₅₁⋊C₃, C₃×(C₁₅₁⋊C₉)⋊C₉, #49144475, …
maximal normal subgroup of	C₉⋊C₉×C₁₅₁⋊C₃, C₃×(C₁₅₁⋊C₉)⋊C₉, #49144475, …
maximal quotient of	C₁₅₁⋊#6855, (C₁₅₁⋊C₉)⋊C₂₇, #49144431, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12231, 20);