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C₂×C₃²×C₂²⋊C₉ #10620100

order	648
isoclinism	isoclinic class of A₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₉ · Schur multiplier (H₂) = C₂×C₃³

Aliases

C₂×C₃²×C₂²⋊C₉

Splittings

derived	C₂² ⋊ C₂×C₃²×C₉
Sylow	C₂³ ⋊ C₃²×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃³	A₄
commutator, hypocenter	C₂²	C₂×C₃²×C₉
Frattini	C₃	C₂×C₃²×A₄
Fitting, socle, prime radical	C₂³×C₃³	C₃
cosocle	C₂²×C₃	C₂×C₃³
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂×C₃³

312 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 162

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃²×(C₂²⋊C₉)⋊C₄, C₃×C₃⋊((C₂²⋊C₉)⋊C₄), C₃⋊(C₃⋊((C₂²⋊C₉)⋊C₄)), …
maximal normal subgroup of	C₃²×(C₂²⋊C₉)⋊C₄, C₃×C₃⋊((C₂²⋊C₉)⋊C₄), C₃⋊(C₃⋊((C₂²⋊C₉)⋊C₄)), …
maximal quotient of	C₃²×C₄×C₂²⋊C₉, C₂×C₃²×Q₈⋊C₉, C₃²×#41⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(648, 619);