C₂₉×#1664 #16815378

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

Aliases

direct product

C₂₉×#1664

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₂₉
prime radical	C₂×D₄×C₂₉	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ G

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

normal subgroups only

This group has 184 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) = 1856

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)(30,31,35,39)(32,40,42,45)(33,38,34,37)(36,43,44,41)(46,47,51,49)(48,54,57,61)(50,58,60,53)(52,59,55,56);(30,32)(31,36)(33,43)(34,41)(35,42)(37,45)(38,40)(39,44)(46,48,51,57)(47,52,49,55)(50,59,60,56)(53,61,58,54);(30,32)(31,36)(33,41)(34,43)(35,42)(37,40)(38,45)(39,44)(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	C₂×C₂₉×#1664, C₂₉×#18987, C₂₉×#18990, …
maximal normal subgroup of	C₂×C₂₉×#1664, C₂₉×#18987, C₂₉×#18990, …
maximal quotient of	C₂₉×#7764, C₂₉×#7765, C₂₉×#7766, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 396);