C₄₇×#10624602 #46804243

order	34263
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₃³×C₄₇ · Schur multiplier (H₂) = C₃³

Aliases

direct product

C₄₇×#10624602

Subgroups

	subgroup	G/H
center, socle	C₃²×C₄₇	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₄₇
prime radical	C₃²×H(3,𝔽₃)×C₄₇	C₃
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₄₇ ◁ C₃⁴×C₄₇ ◁ G

464 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 83
transitive degree	μ_t(G) = 3807

A minimal faithful permutation representation — 3 generators on 83 points:

(1,2,4,3,5,8,7,6,9)(10,11,14,21,27,33,13,16,23)(12,17,28,19,26,22,20,15,24)(18,25,32,31,29,34,30,35,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83);(2,5,6)(10,12,18)(11,15,25)(13,20,30)(14,22,32)(16,26,35)(17,29,27)(19,31,21)(23,28,36)(24,34,33);(2,6,5)(4,8,9)

Conjugacy classes & character table

3431 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34263, 162);