C₁₇×#12461 #16870205

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12433
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#12461

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₇	#466
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₈×Q₈×C₁₇ ◁ G

188 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 65
transitive degree	μ_t(G) = 4352

A minimal faithful permutation representation — 3 generators on 65 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,25)(20,26,28,33)(21,29,31,24)(23,30,32,27)(34,35,39,43)(36,44,46,58)(37,49,51,64)(38,52,50,42)(40,53,54,47)(41,56,57,45)(48,63,62,60)(55,61,59,65);(34,36,45,61,38,48,51,53,39,46,56,65,50,62,37,47)(35,40,49,60,42,55,57,58,43,54,64,63,52,59,41,44);(18,20,22,28)(19,23,25,32)(21,30,31,27)(24,33,29,26)(36,46)(40,54)(44,58)(47,53)(48,62)(55,59)(60,63)(61,65)

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, 5449);