C₁₇×#13458 #16871202

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13371
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#13458

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#476
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₂³×C₁₇	AGL(1,ℤ/8)
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

324 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 53
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 53 points:

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

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, 6446);