C₁₇×#10373 #16868117

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10370
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#10373

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#124
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
socle	C₂²×C₁₇	#393
prime radical	C₂³×C₁₇	#120
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×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)(20,27,29,30)(24,28,32,33)(34,35,37,39)(36,42,43,49)(38,46,45,41)(40,47,48,44);(18,19)(20,28,29,33)(21,31)(22,25)(23,26)(24,30,32,27)(35,39)(40,48)(41,46)(42,49);(18,20)(19,24)(21,30)(22,27)(23,29)(25,33)(26,32)(28,31)(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, 3361);