C₁₇×#13609 #16871353

order	4352
nilpotency class	5
isoclinism	isoclinic class of #13609
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#13609

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#2127
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	#127	C₂³×C₁₇
prime radical	C₁₇×#3220	C₂
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#535 ◁ G

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

normal subgroups only

This group has 348 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)(20,29,31,24)(21,25)(22,27,37,26)(23,28)(30,44,45,38)(32,39,36,40)(33,46,47,49)(34,42)(35,41,48,43);(18,20)(19,24)(21,33)(22,36)(23,32)(25,38)(26,39)(27,29)(28,40)(30,34)(31,37)(35,45)(41,44)(42,49)(43,46)(47,48);(18,21)(19,25)(20,30)(22,35)(23,34)(24,38)(26,43)(27,41)(28,42)(29,44)(31,45)(32,33)(36,47)(37,48)(39,46)(40,49)

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, 6597);