C₉×#398 #10588952

order	576
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂³×C₉ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center	C₂³×C₉	C₂³
commutator	C₂³	C₂³×C₉
Frattini, socle, prime radical, cosocle	C₂³×C₃	C₂³×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

225 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 225 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

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

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 576

A minimal faithful permutation representation — 3 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 834);