C₃²×#2185 #11769234

order	1152
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₂³×C₃

Aliases

	subgroup	G/H
center, socle	C₂²×C₃²	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃²
prime radical	C₃²×#466	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₂²×C₃²×C₄ ◁ C₂²×C₃²×C₈ ◁ G

678 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 678 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.

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

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 576

A minimal faithful permutation representation — 3 generators on 26 points:

(1,2,3)(7,8)(9,10)(12,16)(13,19)(14,21)(17,26)(18,25)(20,23)(22,24);(4,5,6)(11,12,15,18)(13,20,22,26)(14,23,21,17)(16,24,25,19);(8,10)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 3245);