C₁₇×#11483 #16869227

order	4352
nilpotency class	4
isoclinism	isoclinic class of AΣL(1,𝔽₁₆)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#11483

Subgroups

	subgroup	G/H
center	C₈×C₁₇	#99
commutator	C₂³	C₂²×C₈×C₁₇
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₇
socle	C₂×C₁₇	#1459
prime radical	C₁₇×#525	C₄
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₇ ◁ C₂×C₈×C₁₇ ◁ C₂×C₁₇×#131 ◁ G

382 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 126 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)(18,19,21,26,22,27,32,39,23,24,31,35,33,36,43,46)(20,25,28,37,29,38,41,47,30,34,40,44,42,45,48,49);(19,24)(25,34)(27,36)(38,45);(18,20,22,29,23,30,33,42)(19,25,27,38,24,34,36,45)(21,28,32,41,31,40,43,48)(26,37,39,47,35,44,46,49)

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 4471);