C₁₇×#10393 #16868137

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10390
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#10393

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#393
commutator, Frattini, cosocle	C₂⁵	C₂³×C₁₇
prime radical	C₂⁵×C₁₇	C₂³
LCS	G ▷ C₂⁵ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂⁵×C₁₇ ◁ G

526 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 49
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,26)(20,24,31,40)(21,32)(23,28,36,27)(25,34)(29,44)(30,39,46,38)(33,41)(35,42)(37,47)(43,48)(45,49);(18,20)(19,24)(21,33,34,29)(22,31)(23,30)(25,41,32,44)(26,40)(27,38)(28,39)(35,47,48,45)(36,46)(37,42,49,43);(18,21,23,35)(19,25,28,43)(20,29,30,45)(22,34,36,48)(24,37,39,41)(26,32,27,42)(31,33,46,47)(38,44,40,49)

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3381);