C₁₇×#13416 #16871160

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13373
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#13416

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#486
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
socle	C₂×C₁₇	#2041
prime radical	C₁₇×#3150	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#97 ◁ G

442 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 110 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)(20,23)(21,34)(22,41)(24,33)(25,30)(26,32)(27,37)(28,43)(29,42)(31,40)(35,44)(36,49)(38,47)(39,48)(45,46);(18,20)(19,26)(21,35)(22,29)(23,41)(24,28)(25,33)(27,39)(30,42)(31,38)(32,43)(34,37)(36,47)(40,46)(44,49)(45,48);(18,21,22,36,25,40,43,39)(19,27,28,46,30,47,41,35)(20,31,32,49,33,34,29,48)(23,44,42,38,24,45,26,37)

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, 6404);