C₃²×#2679 #11769728

order	1152
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃² · Schur multiplier (H₂) = C₂⁵×C₃×C₄

Aliases

	subgroup	G/H
center, socle	C₂³×C₃²	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃² ◁ G

3000 conjugacy classes of subgroups; only the 672 normal subgroups are shown.

normal subgroups only

This group has 3000 conjugacy classes of subgroups — too many to draw. Only its 672 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) = 288

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 3739);