C₁₇×#9439 #16867183

order	4352
nilpotency class	3
isoclinism	isoclinic class of #9431
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#9439

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#386
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂²×D₄×C₁₇	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

490 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 118 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)(18,19,22,29,34,45,20,32)(21,37,40,44,49,28,35,46)(23,30,33,25,24,31,36,27)(26,43,42,39,47,48,41,38);(19,25,30,29)(20,33)(21,38)(22,36)(26,41,28,44)(27,31,32,45)(37,46,47,42)(39,49);(19,26)(20,33)(21,39)(22,36)(25,41)(27,42)(28,30)(29,44)(31,37)(32,46)(35,40)(38,49)(43,48)(45,47)

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, 2427);