C₁₇×#9481 #16867225

order	4352
nilpotency class	3
isoclinism	isoclinic class of #9471
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#9481

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₂⁵×C₁₇	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

614 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 122 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)(18,19,22,27,23,28,21,34)(20,29,33,40,30,44,31,25)(24,26,36,42,37,38,35,43)(32,45,47,39,46,49,48,41);(18,20,24,32)(19,25,38,39)(21,31,35,48)(22,33,36,47)(23,30,37,46)(26,41,28,40)(27,29,43,49)(34,44,42,45);(19,26)(20,30)(21,35)(22,36)(25,39)(28,38)(29,44)(31,47)(32,46)(33,48)(40,41)(45,49)

Conjugacy classes & character table

629 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 2469);