C₁₇×#9509 #16867253

order	4352
nilpotency class	3
isoclinism	isoclinic class of #9495
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#9509

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#386
commutator	C₂⁴	C₂²×C₄×C₁₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₂²×D₄×C₁₇	C₂×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

524 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 1088

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

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, 2497);