C₁₇×#12448 #16870192

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12416
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#12448

Subgroups

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

218 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 86 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)(18,19,22,25)(20,26,29,33)(21,30,27,24)(23,31,32,28)(35,38)(36,41)(37,40)(42,43)(44,49)(45,48)(46,47);(18,20,27,31,22,29,21,28)(19,23,30,33,25,32,24,26)(34,35,40,43,39,42,37,38)(36,41,47,49,45,48,44,46);(34,36,39,45)(35,41,42,48)(37,44,40,47)(38,46,43,49)

Conjugacy classes & character table

731 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5436);