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C₂₇×C₂²⋊C₉ #11757423

order	972
isoclinism	isoclinic class of A₄
automorphism	?
homology	Abelianization (H₁) = C₉×C₂₇ · Schur multiplier (H₂) = C₂×C₉

Aliases

C₂₇×C₂²⋊C₉

Splittings

C₂² ⋊ C₉×C₂₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₂₇	A₄
commutator, hypocenter	C₂²	C₉×C₂₇
Frattini	C₃×C₉	C₃×A₄
Fitting	C₂²×C₃×C₂₇	C₃
socle, prime radical	C₂²×C₃²	C₃×C₉
cosocle	C₂²×C₃×C₉	C₃²
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₂₇

86 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 486

Conjugacy classes & character table

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

Relationships

derived subgroup of	C₂₇⋊((C₂²⋊C₉)⋊C₂)
maximal subgroup of	C₂₇×(C₂²⋊C₉)⋊C₂, C₂₇⋊((C₂²⋊C₉)⋊C₂), C₂²⋊C₉×D₂₇, …
maximal normal subgroup of	C₂₇×(C₂²⋊C₉)⋊C₂, C₂₇⋊((C₂²⋊C₉)⋊C₂), C₂²⋊C₉×D₂₇, …
maximal quotient of	C₂₇×Q₈⋊C₉, C₂×C₂₇×C₂²⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 148);