C₄₇×#10624598 #46804239

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

Aliases

direct product

C₄₇×#10624598

Subgroups

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

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

normal subgroups only

This group has 302 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) = 101
transitive degree	μ_t(G) = 3807

A minimal faithful permutation representation — 3 generators on 101 points:

(1,2,5,4,8,14,12,7,18)(3,9,13,11,6,15,22,17,25)(10,20,23,21,19,24,27,16,26)(28,29,32,31,34,41,39,45,51)(30,35,46,38,33,42,37,44,40)(36,43,50,48,53,54,49,47,52)(55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(1,3,10,4,11,21,12,22,27)(2,6,16,8,17,20,7,9,19)(5,13,23,14,15,24,18,25,26)(28,30,36)(29,33,43)(31,38,48)(32,40,50)(34,44,53)(35,47,45)(37,49,39)(41,46,54)(42,52,51);(2,7,8)(5,14,18)(6,9,17)(13,15,25)(16,19,20)(23,24,26)

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, 158);