Finite Group Databasebeta

← Prev (#11757815) Next (#11757817) →

C₃×C₉×C₂²⋊C₉ #11757816

order	972
isoclinism	isoclinic class of A₄
automorphism	?
homology	Abelianization (H₁) = C₃×C₉² · Schur multiplier (H₂) = C₂×C₃²×C₉

Aliases

direct product	C₃×C₉×C₂²⋊C₉
unambiguous semidirect product	(C₂²×C₃)⋊C₉²

Splittings

C₂² ⋊ C₃×C₉²

Subgroups

	subgroup	G/H
center, hypercenter	C₃²×C₉	A₄
commutator, hypocenter	C₂²	C₃×C₉²
Frattini	C₃²	C₃²×A₄
Fitting	C₂²×C₃²×C₉	C₃
socle, prime radical	C₂²×C₃³	C₃²
cosocle	C₂²×C₃²	C₃³
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃²×C₉

302 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	C₃⋊(C₉⋊((C₂²⋊C₉)⋊C₂))
maximal subgroup of	C₃×C₉×(C₂²⋊C₉)⋊C₂, C₉×C₃⋊((C₂²⋊C₉)⋊C₂), C₃×C₉⋊((C₂²⋊C₉)⋊C₂), …
maximal normal subgroup of	C₃×C₉×(C₂²⋊C₉)⋊C₂, C₉×C₃⋊((C₂²⋊C₉)⋊C₂), C₃×C₉⋊((C₂²⋊C₉)⋊C₂), …
maximal quotient of	C₃×C₉×Q₈⋊C₉, C₂×C₃×C₉×C₂²⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 541);