C₄₃×#10624745 #44531682

order	31347
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₃³×C₄₃ · Schur multiplier (H₂) = C₃⁵

Aliases

direct product

C₄₃×#10624745

Subgroups

	subgroup	G/H
center, socle	C₃²×C₄₃	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₄₃
prime radical	C₄₃×C₃²⋊H(3,𝔽₃)	C₃
LCS	G ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₄₃ ◁ C₃⁴×C₄₃ ◁ G

500 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 104 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) = 79
transitive degree	μ_t(G) = 3483

A minimal faithful permutation representation — 3 generators on 79 points:

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

Conjugacy classes & character table

3139 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31347, 305);