C₁₇×#7484 #16865228

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

Aliases

direct product

C₁₇×#7484

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1390
commutator	C₂×Q₈	C₄²×C₁₇
Frattini, cosocle	#532	C₂²×C₁₇
prime radical	C₁₇×#532	C₂²
LCS	G ▷ C₂×Q₈ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×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)(18,19,21,26,23,29,38,45)(20,30,32,24,35,40,48,42)(22,28,36,25,39,27,37,43)(31,46,34,44,49,41,33,47);(18,20,22,33,23,35,39,34)(19,24,27,41,29,42,28,46)(21,31,36,48,38,49,37,32)(25,30,26,44,43,40,45,47)

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, 472);