C₂₉×#2080 #16815794

order	3712
nilpotency class	3
isoclinism	isoclinic class of #2031
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#2080

Subgroups

	subgroup	G/H
center	C₄×C₂₉	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
socle	C₂×C₂₉	#397
prime radical	C₂×#41×C₂₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

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

normal subgroups only

This group has 190 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) = 928

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

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#2080, C₂₉×#23649, C₂₉×#23833, …
maximal normal subgroup of	C₂×C₂₉×#2080, C₂₉×#23649, C₂₉×#23833, …
maximal quotient of	C₂₉×#10627, C₂₉×#10628, C₂₉×#10629, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 812);