C₁₇×#9976 #16867720

order	4352
nilpotency class	3
isoclinism	isoclinic class of #9974
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#9976

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₂²×#41×C₁₇	C₂²
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

716 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 102 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)(20,22)(21,23)(24,25)(26,27,32,36)(28,37,41,49)(29,42,46,52)(30,47,31,35)(33,40,50,39)(34,44,53,45)(38,55,56,48)(43,54,57,51);(22,25)(26,28)(27,33)(29,43)(30,40)(31,39)(32,41)(34,51)(35,49)(36,50)(37,47)(38,44)(42,48)(45,56)(46,57)(52,55)(53,54);(18,20)(19,22)(21,24)(23,25)(26,29,32,46)(27,34,36,53)(28,38,41,56)(30,44,31,45)(33,48,50,55)(35,52,47,42)(37,54,49,51)(39,43,40,57)

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, 2964);