C₁₇×#9979 #16867723

order	4352
nilpotency class	3
isoclinism	isoclinic class of #9974
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#9979

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

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

normal subgroups only

This group has 492 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) = 65
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 65 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,23)(21,24)(22,25)(26,29)(27,30)(28,32)(31,33)(34,35,40,44)(36,45,49,57)(37,50,54,60)(38,55,39,43)(41,48,58,47)(42,52,61,53)(46,63,64,56)(51,62,65,59);(18,20,22,27)(19,23,25,30)(21,26,28,33)(24,31,32,29)(34,36)(35,41)(37,51)(38,48)(39,47)(40,49)(42,59)(43,57)(44,58)(45,55)(46,52)(50,56)(53,64)(54,65)(60,63)(61,62);(18,21)(19,24)(20,26)(22,28)(23,29)(25,32)(27,33)(30,31)(34,37,40,54)(35,42,44,61)(36,46,49,64)(38,52,39,53)(41,56,58,63)(43,60,55,50)(45,62,57,59)(47,51,48,65)

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, 2967);