C₁₇×#7270 #16865014

order	4352
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7270

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#331
commutator	C₄²	C₄²×C₁₇
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₇
socle	C₂×C₁₇	#1296
prime radical	C₂³×C₁₇	#101
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

208 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 114 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)(18,19,21,26,24,28,23,38)(20,29,31,40,33,41,30,25)(22,35,34,42,37,48,36,27)(32,46,45,49,47,39,44,43);(18,20,22,32,23,30,36,44,24,33,37,47,21,31,34,45)(19,25,27,39,26,29,35,43,28,40,42,46,38,41,48,49)

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 258);