C₃²×#2207 #11769256

order	1152
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₂²×C₃

Aliases

	subgroup	G/H
center, socle	C₂²×C₃²	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃²
prime radical	C₃²×#493	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₄² ◁ C₃²×C₄×C₈ ◁ G

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

normal subgroups only

This group has 522 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) = 26
transitive degree	μ_t(G) = 576

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 3267);