C₄₇×#731⋊C₉ #46804362

order	34263
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉×C₄₇ · Schur multiplier (H₂) = C₃³

Aliases

direct product	C₄₇×#731⋊C₉
unambiguous semidirect product	#731⋊(C₉×C₄₇)
unambiguous semidirect product	(C₄₇×#731)⋊C₉

Subgroups

	subgroup	G/H
center, socle	C₃²×C₄₇	C₃×H(3,𝔽₃)
commutator	C₃²	C₃²×C₉×C₄₇
Frattini, cosocle	C₃³	C₃³×C₄₇
prime radical	C₃×H(3,𝔽₃)×C₄₇	C₃²
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₄₇ ◁ C₃²×C₉×C₄₇ ◁ G

268 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 83
transitive degree	μ_t(G) = 11421

A minimal faithful permutation representation — 3 generators on 83 points:

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

Conjugacy classes & character table

4935 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34263, 281);