C₁₇×#7488 #16865232

order	4352
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7488

Subgroups

	subgroup	G/H
center	C₄×C₁₇	AΣL(1,𝔽₁₆)
commutator	C₂×D₄	C₄²×C₁₇
Frattini, cosocle	#532	C₂²×C₁₇
socle	C₂×C₁₇	#1390
prime radical	C₁₇×#532	C₂²
LCS	G ▷ C₂×D₄ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#532 ◁ G

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

normal subgroups only

This group has 270 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)(18,19,21,27,24,29,36,43)(20,30,32,42,34,47,48,25)(22,28,35,26,23,37,39,44)(31,41,38,45,49,40,33,46);(18,20,22,33,24,34,23,38)(19,25,28,40,29,42,37,41)(21,31,35,48,36,49,39,32)(26,30,43,46,44,47,27,45)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 476);