C₁₇×#12499 #16870243

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12483
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#12499

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#459
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₂×D₈×C₁₇	D₄
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₈²×C₁₇ ◁ G

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

normal subgroups only

This group has 226 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) = 49
transitive degree	μ_t(G) = 2176

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

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, 5487);