C₁₇×#9493 #16867237

order	4352
nilpotency class	3
isoclinism	isoclinic class of #9471
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#9493

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂⁴×C₁₇	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

458 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 49
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,25,23,26,21,31)(20,27,30,32,28,33,29,24)(34,35,38,42,39,36,40,44)(37,43,46,49,45,41,47,48);(18,20)(19,24,26,32)(21,29)(22,30)(23,28)(25,27,31,33)(34,36,38,44,39,35,40,42)(37,43,47,48,45,41,46,49);(20,28)(24,32)(27,33)(29,30)(34,37)(35,41)(36,43)(38,47)(39,45)(40,46)(42,49)(44,48)

Conjugacy classes & character table

629 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 2481);