C₁₇×#12068 #16869812

order	4352
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#12068

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#442
commutator	C₈	C₂²×C₈×C₁₇
Frattini, cosocle	C₄×C₈	C₂³×C₁₇
socle	C₂×C₁₇	#1580
prime radical	C₁₇×#508	C₄
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂×C₈×C₁₇ ◁ C₁₇×#346 ◁ G

204 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 102 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)(18,19,23,28,24,29,34,40,25,30,22,33,39,20,31,27)(21,32,35,46,36,26,41,43,37,44,38,42,49,45,47,48);(18,20)(19,24)(21,32)(22,27)(23,40)(25,29)(26,36)(28,31)(30,39)(33,34)(35,42)(37,44)(38,46)(41,48)(43,47)(45,49);(18,21,34,41,39,49,23,35,25,37,31,47,24,36,22,38)(19,26,27,46,20,32,33,48,30,45,40,42,29,44,28,43)

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5056);