C₁₇×#9421 #16867165

order	4352
nilpotency class	3
isoclinism	isoclinic class of #9415
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#9421

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#386
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₁₇×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 488 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) = 2176

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

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, 2409);