C₁₇×#9930 #16867674

order	4352
nilpotency class	3
isoclinism	isoclinic class of #9930
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#9930

Subgroups

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

850 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 850 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 33
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 33 points:

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

Conjugacy classes & character table

527 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 2918);