C₉×#352 #10588276

order	576
nilpotency class	4
isoclinism	isoclinic class of AΣL(1,𝔽₁₆)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₉ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center	C₂×C₉	#99
commutator	C₂³	C₂×C₄×C₉
Frattini, prime radical, cosocle	C₂×C₃×D₄	C₂²×C₃
socle	C₂×C₃	C₃×#99
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₉ ◁ C₂²×C₉ ◁ C₂×D₄×C₉ ◁ G

102 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 102 conjugacy classes of subgroups — too many to draw. Only its 39 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) = 144

A minimal faithful permutation representation — 2 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 158);