C₁₇×#7413 #16865157

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×#7413

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

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

normal subgroups only

This group has 178 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)(26,27,29,34,31,36,42,51)(28,37,39,54,38,52,55,50)(30,33,45,49,46,35,43,53)(32,41,47,44,48,56,57,40);(19,22)(20,25)(23,24)(26,28)(27,32,36,48)(29,41)(30,44)(31,38)(33,37,35,52)(34,50,51,54)(39,45)(40,46)(42,56)(43,55)(47,53,57,49)

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, 401);