C₁₇×#13611 #16871355

order	4352
nilpotency class	5
isoclinism	isoclinic class of #13609
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#13611

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#2127
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	C₄⋊Q₈	C₂³×C₁₇
prime radical	C₁₇×#3221	C₂
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#536 ◁ G

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

normal subgroups only

This group has 316 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) = 544

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

Conjugacy classes & character table

425 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6599);