C₁₇×#7405 #16865149

order	4352
nilpotency class	5
isoclinism	isoclinic class of #7402
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7405

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#353
commutator	C₂×C₄²	C₂×C₄×C₁₇
Frattini, cosocle	#391	C₂²×C₁₇
prime radical	C₂³×C₁₇	#99
LCS	G ▷ C₂×C₄² ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#391 ◁ G

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

normal subgroups only

This group has 252 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) = 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)(26,27,29,34,31,36,43,53)(28,37,38,51,40,48,55,56)(30,35,45,52,46,33,42,50)(32,41,47,44,49,54,57,39);(19,22)(20,25)(23,24)(26,28,31,40)(27,32,36,49)(29,41,43,54)(30,44,46,39)(33,48,35,37)(34,51,53,56)(38,42,55,45)(47,52,57,50)

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, 393);