C₁₇×#11916 #16869660

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11915
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#11916

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1533
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	#97	C₂³×C₁₇
prime radical	C₂³×C₁₇	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×M₁₆×C₁₇ ◁ G

274 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 90 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)(18,19,21,27,22,28,35,46,23,25,34,42,37,26,43,44)(20,29,30,47,31,24,38,40,32,41,48,45,36,39,33,49);(18,20,23,32)(19,24,25,39)(21,33,34,38)(22,36,37,31)(26,41,28,29)(27,45,42,47)(30,35,48,43)(40,44,49,46);(19,25)(21,34)(24,39)(26,28)(29,41)(30,48)(33,38)(35,43)

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 4904);