C₁₇×#10663 #16868407

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10012
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#10663

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
socle	C₂²×C₁₇	#399
prime radical	C₂³×C₁₇	C₂²⋊Q₈
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

320 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 114 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)(18,19,23,25,22,20,21,24)(26,27,31,39,30,34,29,33)(28,35,36,32,38,41,37,40);(18,20,22,19)(21,24,23,25)(26,28,29,36,30,38,31,37)(27,32,33,41,34,40,39,35);(18,19,22,20)(21,25,23,24)(26,29,30,31)(27,33,34,39)(28,36,38,37)(32,35,40,41)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3651);