C₃²×#1596 #11768645

order	1152
nilpotency class	3
isoclinism	isoclinic class of #1595
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₂³×C₃

Aliases

	subgroup	G/H
center, socle	C₂²×C₃²	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃²
prime radical	C₃²×#392	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₂²×C₃²×C₄ ◁ G

948 conjugacy classes of subgroups; only the 204 normal subgroups are shown.

normal subgroups only

This group has 948 conjugacy classes of subgroups — too many to draw. Only its 204 normal subgroups are shown.

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

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 22 points:

(1,2,3)(8,12)(9,15)(13,19)(14,16)(17,21)(20,22);(4,5,6)(7,8,10,14)(9,16,15,12)(11,13,18,20)(17,22,21,19);(9,17)(12,19)(15,21)(16,22)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 2656);