C₁₇×#10584 #16868328

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10078
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#10584

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 374 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) = 49
transitive degree	μ_t(G) = 4352

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

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, 3572);