C₁₇×#9991 #16867735

order	4352
nilpotency class	3
isoclinism	isoclinic class of #9986
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#9991

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₂⁴×C₁₇	#41
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

698 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 106 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)(20,22)(21,23)(24,25)(26,27,32,37)(28,38,42,49)(29,43,47,52)(30,36,31,35)(33,41,50,40)(34,45,53,46)(39,48,55,56)(44,57,54,51);(22,25)(26,28,32,42)(27,33,37,50)(29,44,47,54)(30,41,31,40)(34,51,53,57)(35,49,36,38)(39,46,55,45)(43,56,52,48);(18,20)(19,22)(21,24)(23,25)(26,29,32,47)(27,34,37,53)(28,39,42,55)(30,45,31,46)(33,48,50,56)(35,52,36,43)(38,51,49,57)(40,44,41,54)

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, 2979);