C₁₇×#13606 #16871350

order	4352
nilpotency class	5
isoclinism	isoclinic class of #13605
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#13606

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#2127
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	#124	C₂³×C₁₇
prime radical	C₁₇×#3221	C₂
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#536 ◁ G

320 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 86 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)(20,25,30,39)(22,26,32,41)(23,28,33,42)(24,34,37,35)(29,40,43,49)(31,38,45,48)(36,46,47,44);(19,24)(21,32)(22,35)(25,38)(26,28)(30,45)(31,44)(33,34)(36,40)(37,41)(39,49)(43,46);(18,20,23,29)(19,25,28,40)(21,30,33,43)(22,31,35,44)(24,36,26,38)(27,39,42,49)(32,45,34,46)(37,47,41,48)

Conjugacy classes & character table

425 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6594);