C₃×C₄₇×#6872 #46804342

order	34263
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉×C₄₇ · Schur multiplier (H₂) = C₃³

Aliases

direct product

C₃×C₄₇×#6872

Subgroups

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

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

normal subgroups only

This group has 320 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) = 131
transitive degree	μ_t(G) = 11421

A minimal faithful permutation representation — 3 generators on 131 points:

(1,2,3)(85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131);(4,5,9,7,12,24,19,30,46,8,13,23,20,31,45,41,55,68,21,11,27,42,29,51,65,54,72)(6,14,32,17,34,57,39,59,76,18,28,50,40,53,71,64,74,82,16,10,22,38,26,44,63,49,67)(15,33,43,36,58,66,61,77,80,35,52,56,60,73,75,78,83,84,37,25,47,62,48,69,79,70,81);(4,6,15)(5,10,25)(7,17,36)(8,18,35)(9,22,43)(11,28,52)(12,26,48)(13,14,33)(16,37,21)(19,39,61)(20,40,60)(23,32,56)(24,44,66)(27,50,47)(29,53,73)(30,49,70)(31,34,58)(38,62,42)(41,64,78)(45,57,75)(46,67,80)(51,71,69)(54,74,83)(55,59,77)(63,79,65)(68,76,84)(72,82,81)

Conjugacy classes & character table

7191 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34263, 261);