C₁₇×#8796 #16866540

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8790
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#8796

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#382
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂³×C₁₇	#125
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

228 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 118 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)(18,19,22,28,24,29,23,27)(20,26,21,25,31,32,30,33)(34,35,39,45,40,43,38,44)(36,46,48,58,49,41,53,56)(37,50,51,57,52,59,54,42)(47,61,63,60,64,65,62,55);(18,20,23,30,24,31,22,21)(19,25,28,32,29,33,27,26)(34,36,38,48,40,49,39,53)(35,41,44,56,43,46,45,58)(37,47,51,62,52,64,54,63)(42,55,50,65,57,60,59,61);(18,21,22,31,24,30,23,20)(19,26,27,33,29,32,28,25)(34,37)(35,42,43,57)(36,47)(38,51)(39,54)(40,52)(41,55,46,60)(44,50,45,59)(48,62)(49,64)(53,63)(56,65,58,61)

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1784);