C₁₇×#12120 #16869864

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12090
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₇	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₁₇
prime radical	C₁₇×#2021	C₂
LCS	G ▷ C₂×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₁₇ ◁ C₂×C₂²⋊C₄×C₁₇ ◁ G

664 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 664 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.

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

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22)(20,24)(23,25)(26,27)(28,30)(29,31)(32,33);(18,19,21,23)(20,25,24,22)(27,30)(31,33);(28,32)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5108);