C₁₇×#10516 #16868260

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10512
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#10516

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂³×C₁₇	#121
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

364 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 94 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)(20,23)(21,24)(22,25)(26,27,31,35)(28,36,39,51)(29,40,43,33)(30,44,46,34)(32,45,48,38)(37,53,41,52)(42,50,57,55)(47,54,49,56);(18,19)(20,24)(21,23)(22,25)(26,28,31,39)(27,32,35,48)(29,41,43,37)(30,45,46,38)(33,49,40,47)(34,51,44,36)(42,54,57,56)(50,52,55,53);(19,23)(20,21)(24,25)(26,29,30,42,31,43,46,57)(27,33,34,50,35,40,44,55)(28,37,38,54,39,41,45,56)(32,47,36,52,48,49,51,53)

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, 3504);