C₁₇×#13368 #16871112

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13316
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#13368

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₂³×C₁₇	C₂×D₈
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#97 ◁ G

370 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 114 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)(18,19,21,23)(20,24,25,22)(26,27)(28,36)(29,40)(30,45)(31,34)(32,37)(33,44)(35,43)(38,56)(39,53)(41,52)(42,51)(46,50)(47,54)(48,57)(49,55);(18,20,21,25)(19,22,23,24)(29,41)(32,47)(33,49)(37,54)(40,52)(42,57)(44,55)(48,51);(26,28,31,39)(27,32,34,47)(29,42,41,57)(30,46,43,38)(33,50,49,56)(35,51,45,48)(36,52,53,40)(37,55,54,44)

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, 6356);