C₂×C₁₇×#1403 #16871307

order	4352
nilpotency class	5
isoclinism	isoclinic class of #1402
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂×C₁₇×#1403

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	AΣL(1,𝔽₁₆)
commutator	C₂×D₄	C₂²×C₄×C₁₇
Frattini, cosocle	#124	C₂³×C₁₇
prime radical	C₂×C₁₇×H(5,𝔽₂)	C₄
LCS	G ▷ C₂×D₄ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#124 ◁ G

514 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

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

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 35 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35);(3,4,6,10,8,5,12,14)(7,15,17,13,18,11,16,9);(3,5)(4,8)(6,13)(7,11)(9,12)(10,16)(14,17)(15,18)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6551);