C₂₉×#1684 #16815398

order	3712
nilpotency class	3
isoclinism	isoclinic class of #1665
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₉×#1684

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₉	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₂₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ G

144 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 61
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 3 generators on 61 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)(30,31,34,37)(32,38,41,45)(33,42,39,36)(35,43,44,40)(46,47)(48,54)(49,51)(50,58)(52,56)(53,57)(55,61)(59,60);(30,32,39,43,34,41,33,40)(31,35,42,45,37,44,36,38)(47,51)(52,60)(53,58)(54,61);(46,48,49,55)(47,52,51,60)(50,59,57,56)(53,61,58,54)

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#1684, C₂₉×#19123, C₂₉×#19126, …
maximal normal subgroup of	C₂×C₂₉×#1684, C₂₉×#19123, C₂₉×#19126, …
maximal quotient of	C₂₉×#8649, C₂₉×#9216, C₂₉×#9220, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 416);