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D₃×C₈×C₉ #88462

order	432
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = C₂⁴×C₃×D₃ (order 288) · Inn(G) = D₃ · Out(G) = C₂⁴×C₃
homology	Abelianization (H₁) = C₂×C₈×C₉ · Schur multiplier (H₂) = C₂

Aliases

D₃×C₈×C₉

Splittings

Fitting	C₃×C₈×C₉ ⋊ C₂
derived	C₃ ⋊ C₂×C₈×C₉
Sylow	C₃×C₉ ⋊ C₂×C₈

Subgroups

74 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 2 generators on 20 points:

(2,3)(4,5,7,6,8,10,9,11,12);(1,2,3)(13,14,15,17,16,18,19,20)

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×C₉⋊C₁₆, #11720237, D₃×C₉×C₁₆, …
maximal normal subgroup of	D₃×C₉⋊C₁₆, #11720237, D₃×C₉×C₁₆, …
maximal quotient of	D₃×C₉×C₁₆, C₉×#798, C₈×C₉×Dic₃, …
automorphism group of	C₂²×C₇₃, D₃×C₇₃
outer automorphism group of	C₂²×C₇₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 109);