C₁₇×#7522 #16865266

order	4352
nilpotency class	6
isoclinism	isoclinic class of #7519
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7522

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1402
commutator	C₄⋊Q₈	C₂×C₄×C₁₇
Frattini, cosocle	#494	C₂²×C₁₇
prime radical	C₂²×C₁₇	AΣL(1,𝔽₁₆)
LCS	G ▷ C₄⋊Q₈ ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄²×C₁₇ ◁ C₁₇×#494 ◁ G

142 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 30 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)(18,19,22,26,23,28,36,46)(20,27,30,47,31,42,37,45)(21,24,33,38,34,40,48,44)(25,41,43,32,39,35,49,29);(18,20,23,31)(19,24,28,40)(21,32,34,29)(22,30,36,37)(25,42,39,27)(26,43,46,49)(33,35,48,41)(38,47,44,45)

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 510);