C₁₇×#7267 #16865011

order	4352
nilpotency class	4
isoclinism	isoclinic class of #1355
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7267

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#329
commutator	C₄²	C₄²×C₁₇
Frattini, cosocle	C₂×#97	C₂²×C₁₇
socle	C₂×C₁₇	#1295
prime radical	C₂³×C₁₇	#101
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#97 ◁ G

196 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 82 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)(20,29,30,25,32,39,33,41)(22,35,34,42,36,43,37,27)(31,46,45,44,48,40,47,49);(18,20,22,31,23,33,37,47,24,32,36,48,21,30,34,45)(19,25,27,40,26,39,35,49,28,41,42,46,38,29,43,44)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 255);