C₄₇×#10624760 #46804401

order	34263
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₃³×C₄₇ · Schur multiplier (H₂) = C₃⁵

Aliases

direct product

C₄₇×#10624760

Subgroups

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

456 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 128
transitive degree	μ_t(G) = 3807

A minimal faithful permutation representation — 3 generators on 128 points:

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

Conjugacy classes & character table

2679 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34263, 320);