C₄₇×#10624746 #46804387

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

Aliases

direct product

C₄₇×#10624746

Subgroups

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

470 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 3807

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

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

Conjugacy classes & character table

3431 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34263, 306);