C₁₇×#8794 #16866538

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8794
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₁₇×#8794

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#382
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂³×C₁₇	#124
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

270 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 57
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 57 points:

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

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1782);