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C₂³×D₃×C₉ #88910

order	432
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product	C₂³×D₃×C₉
unambiguous semidirect product	C₃⋊(C₂⁴×C₉)
unambiguous semidirect product	(C₂×C₃)⋊(C₂³×C₉)

Splittings

Fitting	C₂³×C₃×C₉ ⋊ C₂
derived	C₃ ⋊ C₂⁴×C₉
Sylow	C₃×C₉ ⋊ C₂⁴

Subgroups

434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 4 generators on 18 points:

(1,2)(3,4)(5,6)(8,9)(10,14,18,12,17,13,15,11,16);(5,6)(7,8,9);(3,4);(1,2)

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×(C₂×D₃)⋊Dic₉, D₃×#3676, #11721286, …
maximal normal subgroup of	C₂×(C₂×D₃)⋊Dic₉, D₃×#3676, #11721286, …
maximal quotient of	C₂²×C₉×Dic₆, C₂²×C₄×D₃×C₉, C₂²×C₉×D₁₂, …
automorphism group of	C₁₉×C₃⋊C₈, C₄×D₃×C₁₉, C₁₉×#67

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 557);