C₁₇×#13342 #16871086

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13316
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#13342

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₁₇×#3150	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#97 ◁ G

558 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 53
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 53 points:

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

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, 6330);