C₁₇×#7429 #16865173

order	4352
nilpotency class	5
isoclinism	isoclinic class of #7412
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7429

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#354
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

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

normal subgroups only

This group has 196 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)(19,22,23,24)(26,27,29,34,31,36,42,52)(28,37,38,51,40,48,54,57)(30,33,44,50,45,35,43,53)(32,46,47,39,49,41,56,55);(18,19)(20,24)(21,23)(22,25)(26,28,30,39,31,40,45,55)(27,32,35,48,36,49,33,37)(29,41,43,38,42,46,44,54)(34,51,50,56,52,57,53,47)

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, 417);