C₁₇×#10670 #16868414

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10012
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#10670

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
socle	C₂²×C₁₇	#399
prime radical	C₂³×C₁₇	#123
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

316 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 114 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)(18,19,21,23,22,25,20,24)(26,27,32,37,31,36,30,35)(28,38,47,33,41,49,40,50)(29,42,46,52,45,34,44,53)(39,51,43,48,55,56,54,57);(19,23)(20,21)(24,25)(26,28,30,47,31,41,32,40)(27,33,35,49,36,50,37,38)(29,43,44,55,45,54,46,39)(34,51,52,48,42,56,53,57);(18,19,22,25)(20,23,21,24)(26,29,31,45)(27,34,36,42)(28,39,41,55)(30,44,32,46)(33,48,50,57)(35,52,37,53)(38,51,49,56)(40,54,47,43)

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, 3658);