C₁₇×#8915 #16866659

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

Aliases

direct product

C₁₇×#8915

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

396 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 134 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)(18,19,21,20)(22,23,28,33)(24,34,25,36)(26,32,27,31)(29,37,30,35)(39,43)(41,48)(44,52)(45,49)(46,50)(51,53);(18,20,21,19)(22,24,28,25)(23,29,33,30)(26,37,27,35)(31,36,32,34)(38,39,42,45)(40,44,47,53)(41,49,48,43)(46,51,50,52);(22,25,28,24)(23,30,33,29)(26,37,27,35)(31,36,32,34)(38,40,42,47)(39,44,45,53)(41,50,48,46)(43,51,49,52)

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, 1903);