C₁₇×#10369 #16868113

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10362
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#10369

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#393
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂³×C₁₇	#120
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

364 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 106 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)(18,19,21,24)(20,27)(22,26,23,31)(25,28)(29,32)(30,33)(34,35,37,39)(36,42,43,49)(38,46,45,41)(40,47,48,44);(19,24)(20,28,30,29)(25,33,32,27)(26,31)(35,39)(40,48)(41,46)(42,49);(18,20)(19,25)(21,30)(22,28)(23,29)(24,32)(26,33)(27,31)(34,36,37,43)(35,40,39,48)(38,47,45,44)(41,49,46,42)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3357);