C₂₉×#1663 #16815377

order	3712
nilpotency class	3
isoclinism	isoclinic class of #1655
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#1663

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₉	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₂₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ G

172 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 60 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)(30,31,36,40)(32,41,43,44)(33,42,37,45)(34,39,35,38)(46,47,51,49)(48,54,57,61)(50,58,60,53)(52,59,55,56);(30,32)(31,37)(33,40)(34,45)(35,42)(36,43)(38,44)(39,41)(46,48,51,57)(47,52,49,55)(50,59,60,56)(53,61,58,54);(30,33,36,37)(31,32,40,43)(34,44,35,41)(38,42,39,45)(46,49,51,47)(48,55,57,52)(50,53,60,58)(54,59,61,56)

Conjugacy classes & character table

580 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#7526, C₂×C₂₉×#1663, C₂₉×#18990, …
maximal normal subgroup of	C₂₉×#7526, C₂×C₂₉×#1663, C₂₉×#18990, …
maximal quotient of	C₂₉×#7763, C₂₉×#7768, C₂₉×#7772, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 395);