C₄₇×#10624700 #46804341

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

Aliases

direct product

C₄₇×#10624700

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

344 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 152 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:

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

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, 260);