C₃×C₄₃×#6909 #44531861

order	31347
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₃⁴×C₄₃ · Schur multiplier (H₂) = C₃⁶

Aliases

direct product

C₃×C₄₃×#6909

Subgroups

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

1196 conjugacy classes of subgroups; only the 476 normal subgroups are shown.

normal subgroups only

This group has 1196 conjugacy classes of subgroups — too many to draw. Only its 476 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) = 73
transitive degree	μ_t(G) = 3483

A minimal faithful permutation representation — 4 generators on 73 points:

(1,2,3)(31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73);(4,5,8)(6,12,17)(7,11,18)(9,19,15)(10,22,16)(13,24,27)(14,21,28)(20,30,26)(23,29,25);(4,6,13)(5,9,20)(7,15,25)(8,17,27)(10,12,23)(11,21,24)(14,26,16)(18,19,29)(22,28,30);(6,14,15)(9,12,21)(13,25,26)(17,28,19)(20,24,23)(27,29,30)

Conjugacy classes & character table

4515 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31347, 484);