C₁₇×#7505 #16865249

order	4352
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#7505

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#354
commutator	C₄²	C₄²×C₁₇
Frattini, cosocle	C₂×C₄⋊Q₈	C₂²×C₁₇
prime radical	C₂³×C₁₇	#99
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×C₄⋊Q₈ ◁ G

260 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 1088

A minimal faithful permutation representation — 2 generators on 53 points:

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

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 493);