C₂₉×#10624627 #35231968

order	21141
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₃³×C₂₉ · Schur multiplier (H₂) = C₃²

Aliases

direct product

C₂₉×#10624627

Subgroups

	subgroup	G/H
center, socle	C₃²×C₂₉	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₂₉
prime radical	C₂₉×#6856	C₃
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₂₉ ◁ C₃²×C₉×C₂₉ ◁ G

214 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 74 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) = 7047

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

(1,2,6,16,9,24,5,10,19)(3,11,17,25,22,27,13,7,20)(4,14,26,12,8,23,15,21,18)(28,29,33,32,35,42,31,36,41)(30,34,43,39,45,51,38,46,40)(37,47,50,48,44,52,49,53,54)(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);(1,3,12,16,25,15,5,13,4)(2,7,21,9,11,14,10,22,8)(6,17,23,24,27,18,19,20,26)(28,30,37,32,39,48,31,38,49)(29,34,44,35,45,53,36,46,47)(33,40,50,42,43,52,41,51,54);(1,4,13,5,15,25,16,12,3)(2,8,22,10,14,11,9,21,7)(6,18,17,19,23,20,24,26,27)(29,35,36)(33,41,42)(34,45,46)(40,51,43)(44,53,47)(50,54,52)

Conjugacy classes & character table

2117 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21141, 187);