C₁₇×#12067 #16869811

order	4352
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#12067

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#442
commutator	C₈	C₂²×C₈×C₁₇
Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₂×C₁₇×D₁₆	C₄
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₁₇×#322 ◁ G

246 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 41
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 3 generators on 41 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,24,22,20,23,25)(26,27,29,32,30,35,40,34)(28,36,39,33,38,31,37,41);(27,31)(28,37)(29,40)(32,33)(34,41)(35,36)(38,39);(18,20,21,25,22,19,23,24)(27,32,35,34)(28,38)(31,33,36,41)(37,39)

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5055);