D₅×A₄⋊AGL(1,ℤ/9) #72247649

order	6480
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂²×C₃

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₅×C₉×A₄	C₂²×C₃
Frattini	C₃	C₃×D₅×C₃⋊S₄
Fitting	C₂²×C₅×3₋¹⁺²	C₂×D₃
socle	C₂²×C₃×C₅	C₂×C₃×C₃⋊D₃
LCS	G ▷ C₅×C₉×A₄
UCS	C₁

636 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 180

A minimal faithful permutation representation — 3 generators on 18 points:

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

maximal subgroup of	D₅×S₄×AGL(1,ℤ/9), #72254833, AGL(1,𝔽₅)×A₄⋊AGL(1,ℤ/9)
maximal normal subgroup of	D₅×S₄×AGL(1,ℤ/9), #72254833, AGL(1,𝔽₅)×A₄⋊AGL(1,ℤ/9)

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,4)(2,3)(6,7)(8,9)(10,16,18,12,14,13,17,11,15), (2,4)(5,6,8,9,7)(11,13)(12,17)(14,15)(16,18), (2,3,4));