C₁₇×#8492 #16866236

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8491
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#8492

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#379
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₁₇×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

692 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 142 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)(19,22,23,24)(26,27)(28,36,39,32)(29,40,42,49)(30,35)(31,34)(33,41,47,43)(37,52)(38,51,56,46)(44,48)(45,53)(50,55)(54,57);(18,19)(20,24)(21,23)(22,25)(26,28,31,39)(27,32,34,36)(29,37,42,54)(30,38,44,56)(33,45,47,50)(35,46,48,51)(40,57,49,52)(41,53,43,55);(20,25)(22,24)(26,29)(27,33)(28,37)(30,43)(31,42)(32,45)(34,47)(35,49)(36,50)(38,55)(39,54)(40,48)(41,44)(46,52)(51,57)(53,56)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1480);