C₁₇×#7507 #16865251

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

Aliases

direct product

C₁₇×#7507

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#353
commutator	C₄²	C₄²×C₁₇
Frattini, cosocle	#532	C₂²×C₁₇
socle	C₂×C₁₇	#1393
prime radical	C₁₇×#532	C₂²
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#532 ◁ G

266 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 66 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 — 2 generators on 49 points:

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

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, 495);