C₁₇×#12308 #16870052

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12307
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#12308

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1616
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₇
prime radical	C₂³×C₁₇	AGL(1,ℤ/8)
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×M₁₆×C₁₇ ◁ G

274 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 49
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 49 points:

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

Conjugacy classes & character table

425 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5296);