C₁₇×#8795 #16866539

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8794
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₁₇×#8795

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#382
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂³×C₁₇	#124
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

270 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 126 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)(19,24)(20,25)(21,22)(26,27)(28,36,40,32)(29,41,44,55)(30,35)(31,34)(33,43,49,52)(37,45)(38,53)(39,50,51,47)(42,56)(46,54)(48,57);(18,19,21,24,23,25,22,20)(26,28,37,51,31,40,30,39)(27,32,45,50,34,36,35,47)(29,42,52,54,44,38,43,57)(33,48,55,56,49,46,41,53);(18,20,21,19,23,24,22,25)(26,29)(27,33,34,49)(28,38)(30,43)(31,44)(32,46,36,48)(35,41,45,55)(37,52)(39,54)(40,42)(47,56,50,53)(51,57)

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, 1783);