C₁₇×#7759 #16865503

order	4352
nilpotency class	3
isoclinism	isoclinic class of #7734
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#7759

Subgroups

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

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

normal subgroups only

This group has 456 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) = 49
transitive degree	μ_t(G) = 4352

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

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, 747);