C₁₇×#12533 #16870277

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12525
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#12533

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₇	#493
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₈²×C₁₇ ◁ G

238 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 94 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)(20,26,27,33)(21,29,30,24)(23,31,32,28)(34,35)(36,44)(37,40)(38,51)(39,52)(41,47)(42,45)(43,50)(46,56)(48,63)(49,64)(53,61)(54,60)(55,65)(57,59)(58,62);(18,20,21,28,22,27,30,31)(19,23,24,26,25,32,29,33)(35,40)(41,53)(42,54)(43,52)(44,56)(51,64)(55,57)(58,63);(20,27)(23,32)(26,33)(28,31)(34,36,45,59,39,48,49,61,37,46,60,65,50,62,38,47)(35,41,51,58,43,55,54,56,40,53,64,63,52,57,42,44)

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5521);