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(C₁₃₉⋊C₉)⋊C₉ #26014602

order	11259
automorphism	?
homology	Abelianization (H₁) = C₃×C₉ · Schur multiplier (H₂) = C₃

Aliases

unambiguous semidirect product

(C₁₃₉⋊C₉)⋊C₉

Splittings

C₁₃₉ ⋊ C₉⋊C₉

Subgroups

	subgroup	G/H
center, Frattini	C₃²	C₃×C₁₃₉⋊C₃
commutator	C₃×C₁₃₉	C₃×C₉
Fitting	C₃×C₉×C₁₃₉	C₃
socle, prime radical, cosocle	C₃²×C₁₃₉	C₃²
hypercenter	C₃×C₉	C₁₃₉⋊C₃
hypocenter	C₁₃₉	C₉⋊C₉
LCS	G ▷ C₃×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₃² ◁ C₃×C₉

34 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

3^4,139|a^3=d,b^3=c,b^a=bc,e^b=e^96

Conjugacy classes & character table

1275 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉⋊C₉×C₁₃₉⋊C₃, C₃×(C₁₃₉⋊C₉)⋊C₉, #46798539, …
maximal normal subgroup of	C₉⋊C₉×C₁₃₉⋊C₃, C₃×(C₁₃₉⋊C₉)⋊C₉, #46798539, …
maximal quotient of	C₁₃₉⋊#6855, (C₁₃₉⋊C₉)⋊C₂₇, #46798495, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11259, 20);