C₂₉×#2047 #16815761

order	3712
nilpotency class	3
isoclinism	isoclinic class of #2018
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#2047

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
prime radical	C₂³×C₂₉	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

256 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 65
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 generators on 65 points:

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

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#12167, C₂₉×#12168, C₂₉×#12169, …
maximal normal subgroup of	C₂₉×#12167, C₂₉×#12168, C₂₉×#12169, …
maximal quotient of	C₂₉×#10446, C₂₉×#10447, C₂₉×#10454, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 779);