C₁₇×#8753 #16866497

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8746
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#8753

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#381
commutator	C₂⁴	C₂²×C₄×C₁₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₂⁴×C₁₇	C₂²×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

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

normal subgroups only

This group has 566 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) = 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)(20,24,25,22)(21,23)(26,27,30,35,31,34,44,49)(28,36,38,50,39,32,43,46)(29,40,42,54,41,33,47,48)(37,45,53,56,52,51,55,57);(26,28,31,39)(27,32,34,36)(29,37,41,52)(30,43,44,38)(33,45,40,51)(35,50,49,46)(42,55,47,53)(48,57,54,56);(18,20)(19,22)(21,25)(23,24)(26,29)(27,33,34,40)(28,37)(30,42)(31,41)(32,45,36,51)(35,48,49,54)(38,53)(39,52)(43,55)(44,47)(46,56,50,57)

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, 1741);