C₁₇×#7368 #16865112

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

Aliases

direct product

C₁₇×#7368

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

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

normal subgroups only

This group has 136 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)(18,19,21,27,23,28,37,45,24,29,36,46,22,26,38,43)(20,30,31,44,33,25,39,40,34,41,47,49,32,42,35,48);(18,20,22,32,24,34,23,33)(19,25,28,41,29,42,26,30)(21,35,37,31,36,39,38,47)(27,44,43,48,46,49,45,40)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 356);