C₁₇×#7524 #16865268

order	4352
nilpotency class	6
isoclinism	isoclinic class of #7523
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7524

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1404
commutator	#125	C₂×C₄×C₁₇
Frattini, cosocle	#490	C₂²×C₁₇
prime radical	C₁₇×#127	D₄
LCS	G ▷ #125 ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄²×C₁₇ ◁ C₁₇×#490 ◁ G

134 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 30 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)(20,28)(21,32,34,25)(22,27)(23,26,36,44)(24,29,39,47)(30,46)(31,45,37,49)(33,40,48,41)(35,42,38,43);(18,20,22,30)(19,24,27,41)(21,33,35,29)(23,37,36,31)(25,28,43,46)(26,40,44,39)(32,49,42,45)(34,47,38,48)

Conjugacy classes & character table

323 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 512);