C₁₇×#13373 #16871117

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13373
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#13373

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#486
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
socle	C₂×C₁₇	#2023
prime radical	C₂×C₁₇×#135	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#97 ◁ G

364 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 544

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)(20,29,31,46)(21,34)(22,27)(23,39)(24,28)(25,32,41,48)(26,38)(30,47,33,43)(35,45)(36,44,49,40)(37,42);(20,30,31,33)(21,35)(25,40,41,44)(26,42)(29,43,46,47)(32,49,48,36)(34,45)(37,38);(18,20)(19,25)(21,36)(22,33)(23,30)(24,31)(26,43)(27,44)(28,41)(29,45)(32,37)(34,46)(35,49)(38,48)(39,40)(42,47)

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, 6361);