C₁₇×#13457 #16871201

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

Aliases

direct product

C₁₇×#13457

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

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

normal subgroups only

This group has 356 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) = 37
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(23,28,30,37)(24,32)(25,26)(29,33,31,36)(34,35);(18,19)(20,21)(23,29,30,31)(28,36,37,33);(19,21)(22,23,26,29,27,30,25,31)(24,33,32,28,35,36,34,37)

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, 6445);