C₂₉×#1636 #16815350

order	3712
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#1636

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

188 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 72 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)(30,31,35,38)(32,39,41,44)(33,37,34,42)(36,43,45,40)(46,47,52,56)(48,57,49,60)(50,55,51,54)(53,59,61,58);(30,32)(31,36)(33,40)(34,43)(35,41)(37,44)(38,45)(39,42)(46,48,52,49)(47,53,56,61)(50,59,51,58)(54,60,55,57);(30,33,35,34)(31,37,38,42)(32,40,41,43)(36,44,45,39)(46,49,52,48)(47,53,56,61)(50,58,51,59)(54,60,55,57)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#1636, C₂₉×#18494, C₂₉×#18519, …
maximal normal subgroup of	C₂×C₂₉×#1636, C₂₉×#18494, C₂₉×#18519, …
maximal quotient of	C₂₉×#7763, C₂₉×#7769, C₂₉×#7771, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 368);