C₁₇×#8772 #16866516

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8760
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#8772

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#381
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂²×D₄×C₁₇	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 446 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) = 544

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)(18,19,21,24,22,20,25,23)(26,27)(28,35,37,31)(29,34)(30,33)(32,36,39,41)(38,40);(26,28)(27,31)(29,36)(30,37)(32,34)(33,35)(38,41)(39,40);(18,20)(19,22)(21,23)(24,25)(26,28)(27,32,33,39)(29,36)(30,37)(31,34,35,40)(38,41)

Conjugacy classes & character table

731 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1760);