C₂×C₁₇×#2196 #16891287

order	4352
nilpotency class	4
isoclinism	isoclinic class of #2196
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁷

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₇	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×D₄	C₂⁴×C₁₇
LCS	G ▷ C₂×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₁₇ ◁ C₂²×D₄×C₁₇ ◁ G

1956 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 1956 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.

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

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 272

A minimal faithful permutation representation — 4 generators on 27 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 26531);