C₃²×#1699 #11768748

order	1152
nilpotency class	3
isoclinism	isoclinic class of #1685
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

	subgroup	G/H
center, socle	C₂²×C₃²	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₃²
prime radical	C₂×C₃²×D₄	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₄² ◁ G

480 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 192 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) = 576

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 2759);