C₁₇×#7261 #16865005

order	4352
nilpotency class	4
isoclinism	isoclinic class of #1347
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7261

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#102
commutator	C₂×C₈	C₄²×C₁₇
Frattini, cosocle	C₂³×C₈	C₂²×C₁₇
socle	C₂²×C₁₇	#340
prime radical	C₂⁴×C₁₇	Q₁₆
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ C₂³×C₈×C₁₇ ◁ G

320 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 57
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 2 generators on 57 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,22)(21,24)(23,25)(26,27,30,35,32,36,31,46)(28,37,39,53,40,54,47,51)(29,41,43,52,45,56,44,34)(33,42,48,55,50,57,49,38);(19,22,24,23)(26,28,30,39,32,40,31,47)(27,33,35,48,36,50,46,49)(29,42,43,55,45,57,44,38)(34,51,41,37,52,53,56,54)

Conjugacy classes & character table

986 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 249);