C₁₇×#8797 #16866541

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×#8797

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

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, 1785);