C₁₇×#8509 #16866253

order	4352
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#8509

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	#120
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

656 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 158 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) = 53
transitive degree	μ_t(G) = 4352

A minimal faithful permutation representation — 3 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,28,31,26,25,27,30)(24,29,35,37,33,32,34,36)(39,43,45,48)(44,52,53,51);(22,24,26,33)(23,29,25,32)(27,35,28,34)(30,37,31,36)(38,39)(40,44)(41,48)(42,45)(43,50)(46,51)(47,53)(49,52);(19,21)(22,25,26,23)(24,32,33,29)(27,30,28,31)(34,36,35,37)(38,40,42,47)(39,44,45,53)(41,49,50,46)(43,51,48,52)

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, 1497);