C₁₇×#10045 #16867789

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10038
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#10045

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂³×C₁₇	#121
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 444 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) = 65
transitive degree	μ_t(G) = 2176

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)(20,26)(21,29)(22,25)(23,28)(24,31)(27,33)(30,32)(34,35,40,45)(36,46,49,57)(37,42,53,60)(38,44,39,43)(41,50,56,48)(47,62,63,58)(51,65,64,55)(52,61,54,59);(23,32)(26,33)(34,36,40,49)(35,41,45,56)(37,51,53,64)(38,50,39,48)(42,58,60,62)(43,57,44,46)(47,54,63,52)(55,61,65,59);(18,20)(19,23)(21,30)(22,27)(24,33)(25,32)(26,29)(28,31)(34,37,40,53)(35,42,45,60)(36,47,49,63)(38,52,39,54)(41,55,56,65)(43,59,44,61)(46,58,57,62)(48,51,50,64)

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, 3033);