C₁₇×#7356 #16865100

order	4352
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#7356

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#353
commutator	C₄²	C₂×C₈×C₁₇
Frattini, cosocle	#423	C₂²×C₁₇
socle	C₂×C₁₇	#1318
prime radical	C₁₇×#532	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#423 ◁ G

202 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 46 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 — 2 generators on 49 points:

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

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 344);