C₁₇×#10031 #16867775

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10026
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#10031

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂³×C₁₇	#121
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 468 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) = 49
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 3 generators on 49 points:

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

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, 3019);