D₉×#5934 #72245462

order	3456
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂⁴

Aliases

Fitting	C₉×H(5,𝔽₂) ⋊ C₂×D₃
derived	C₉×#997 ⋊ C₂²

	subgroup	G/H
center, hypercenter	C₂	D₉×#1020
commutator, cosocle, hypocenter	C₉×#997	C₂²
Frattini, socle	C₂×C₃	D₃×#1020
Fitting	C₉×H(5,𝔽₂)	C₂×D₃
LCS	G ▷ C₉×#997
UCS	C₁ ◁ C₂

1363 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 1363 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.

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

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 2 generators on 17 points:

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

maximal subgroup of	AGL(1,ℤ/9)×#5934
maximal normal subgroup of	AGL(1,ℤ/9)×#5934

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

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