C₁₇×#7736 #16865480

order	4352
nilpotency class	3
isoclinism	isoclinic class of #7734
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#7736

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₁₇×#2011	C₂
LCS	G ▷ C₂×C₄² ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

560 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 41
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 3 generators on 41 points:

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

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, 724);