C₁₇×#7483 #16865227

order	4352
nilpotency class	5
isoclinism	isoclinic class of #7481
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7483

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1390
commutator	C₂×Q₈	C₄²×C₁₇
Frattini, cosocle	C₂×C₄⋊Q₈	C₂²×C₁₇
prime radical	C₂³×C₁₇	#99
LCS	G ▷ C₂×Q₈ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂³×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×C₄⋊Q₈ ◁ G

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

normal subgroups only

This group has 262 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)(18,19,21,26,23,27,35,45)(20,29,31,24,33,39,48,40)(22,28,37,25,38,42,34,43)(30,46,32,44,49,41,36,47);(18,20)(19,24,27,40)(21,30)(22,36)(23,33)(25,29,43,39)(26,44,45,47)(28,46,42,41)(31,34)(32,38)(35,49)(37,48)

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, 471);