C₄₇×#10624752 #46804393

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

Aliases

direct product

C₄₇×#10624752

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

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

normal subgroups only

This group has 446 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) = 74
transitive degree	μ_t(G) = 1269

A minimal faithful permutation representation — 3 generators on 74 points:

(1,2,6,5,4,8,16,9,15)(3,10,17,14,7,18,13,12,23)(11,21,25,22,20,26,24,19,27)(28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74);(1,3,11,5,14,22,16,13,24)(2,7,19,4,12,21,9,10,20)(6,17,25,8,18,26,15,23,27);(1,4,15,5,9,6,16,2,8)(3,12,23,14,10,17,13,7,18)(11,21,27,22,20,25,24,19,26)

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, 312);