C₁₇×#10668 #16868412

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

Aliases

direct product

C₁₇×#10668

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)(18,19,20,24,22,25,21,23)(26,27,30,35,31,36,32,46)(28,37,39,49,41,53,40,33)(29,42,44,52,45,34,47,51)(38,54,43,57,55,50,56,48);(19,23)(20,21)(24,25)(26,28,32,39,31,41,30,40)(27,33,46,37,36,49,35,53)(29,43,47,55,45,56,44,38)(34,50,52,48,42,54,51,57);(18,19,22,25)(20,23,21,24)(26,29,31,45)(27,34,36,42)(28,38,41,55)(30,44,32,47)(33,48,49,57)(35,51,46,52)(37,54,53,50)(39,43,40,56)

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, 3656);