C₄₇×#10624698 #46804339

order	34263
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉×C₄₇ · Schur multiplier (H₂) = C₃⁴

Aliases

direct product

C₄₇×#10624698

Subgroups

	subgroup	G/H
center, socle	C₃²×C₄₇	C₃×H(3,𝔽₃)
commutator	C₃²	C₃²×C₉×C₄₇
Frattini, cosocle	C₃³	C₃³×C₄₇
prime radical	C₃²×H(3,𝔽₃)×C₄₇	C₃
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₄₇ ◁ C₃⁴×C₄₇ ◁ G

512 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 152 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:

(1,2,4,3,5,7,6,8,9)(10,11,14)(12,18,28)(13,17,24)(15,23,20)(16,27,22)(19,29,32)(21,26,35)(25,33,31)(30,34,36)(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);(10,12,19)(11,15,25)(13,21,30)(14,23,32)(16,26,34)(17,18,29)(20,31,22)(24,28,36)(27,35,33);(11,16,17)(14,24,27)(15,26,18)(23,28,35)(25,34,29)(32,36,33)

Conjugacy classes & character table

4935 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34263, 258);