C₁₇×#9196 #16866940

order	4352
nilpotency class	3
isoclinism	isoclinic class of #9183
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#9196

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂⁴×C₁₇	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 134 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 — 3 generators on 57 points:

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

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 2184);