C₁₇×#11911 #16869655

order	4352
nilpotency class	4
isoclinism	isoclinic class of #1355
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#11911

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#329
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	#97	C₂³×C₁₇
socle	C₂×C₁₇	C₂×#329
prime radical	C₁₇×#532	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#97 ◁ G

318 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 106 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 — 3 generators on 49 points:

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

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 4899);