C₁₇×#9429 #16867173

order	4352
nilpotency class	3
isoclinism	isoclinic class of #9415
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#9429

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#386
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₁₇×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

508 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 57
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 57 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,25,22,20,21,24)(26,27,31,35,32,37,30,36)(28,38,41,48,42,51,40,33)(29,43,45,34,46,49,44,50)(39,47,54,56,55,57,53,52);(18,20,22,19)(21,24,23,25)(26,28)(27,33,37,48)(29,39)(30,40)(31,41)(32,42)(34,47,50,57)(35,38,36,51)(43,52,49,56)(44,53)(45,54)(46,55);(21,23)(24,25)(26,29,32,46)(27,34,37,50)(28,39,42,55)(30,45,31,44)(33,47,48,57)(35,43,36,49)(38,52,51,56)(40,54,41,53)

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, 2417);