C₁₇×#10644 #16868388

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10637
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#10644

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#397
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂³×C₁₇	#123
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

298 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 102 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)(18,19,22,24,20,23,21,25)(26,27)(28,36,39,49)(29,33)(30,34)(31,35)(32,38,46,43)(37,52,40,51)(41,47)(42,48)(44,50)(45,54,56,53)(55,57);(19,23)(24,25)(26,28,31,39)(27,32,35,46)(29,40,42,37)(30,43,44,38)(33,45,48,56)(34,49,50,36)(41,53,55,54)(47,52,57,51);(19,24)(21,22)(23,25)(26,29,30,41,31,42,44,55)(27,33,34,47,35,48,50,57)(28,37,38,53,39,40,43,54)(32,45,36,51,46,56,49,52)

Conjugacy classes & character table

629 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3632);