Finite Group Databasebeta

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C₂×C₉×C₃⋊(C₃⋊D₃) #11758131

order	972
isoclinism	isoclinic class of C₃⋊(C₃⋊D₃)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂×C₃³

Aliases

direct product	C₂×C₉×C₃⋊(C₃⋊D₃)
unambiguous semidirect product	(C₂×C₃)⋊(C₉×C₃⋊D₃)

Splittings

Fitting	C₂×C₃³×C₉ ⋊ C₂
derived	C₃³ ⋊ C₂²×C₉
Sylow	C₃³×C₉ ⋊ C₂²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	C₃⋊(C₃⋊D₃)
commutator, hypocenter	C₃³	C₂²×C₉
Frattini	C₃	C₂×C₃×C₃⋊(C₃⋊D₃)
Fitting	C₂×C₃³×C₉	C₂
socle	C₂×C₃⁴	C₂×C₃
prime radical	C₂×C₃×C₃⋊(C₃⋊D₃)	C₃
cosocle	C₃⁴	C₂²×C₃
LCS	G ▷ C₃³
UCS	C₁ ◁ C₂×C₉

732 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 324

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₉×#6289, C₉×#6291, C₉×#6292, …
maximal normal subgroup of	C₉×#6289, C₉×#6291, C₉×#6292, …
maximal quotient of	C₉×#6308, C₄×C₉×C₃⋊(C₃⋊D₃), C₉×C₄⋊(C₃⋊(C₃⋊D₃)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 856);