C₁₇×#7369 #16865113

order	4352
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7369

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#354
commutator	C₄²	C₂×C₈×C₁₇
Frattini, cosocle	#423	C₂²×C₁₇
socle	C₂×C₁₇	#1324
prime radical	C₂³×C₁₇	#101
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#423 ◁ G

132 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 46 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 — 2 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,27,23,26,36,43,24,29,37,46,22,28,38,45)(20,30,32,47,34,25,39,40,31,41,48,44,33,42,35,49);(18,20,22,33,24,31,23,34)(19,25,28,30,29,42,26,41)(21,35,36,32,37,39,38,48)(27,44,43,49,46,47,45,40)

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, 357);