C₂₉×#2098 #16815812

order	3712
nilpotency class	3
isoclinism	isoclinic class of #2010
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#2098

Subgroups

	subgroup	G/H
center	C₄×C₂₉	#127
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
socle	C₂×C₂₉	#399
prime radical	C₂×#41×C₂₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

210 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 80 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)(30,31,34,39,35,40,36,50)(32,41,43,53,45,57,44,37)(33,46,48,56,49,38,51,55)(42,58,47,61,59,54,60,52);(30,32,36,43,35,45,34,44)(31,37,50,41,40,53,39,57)(33,47,51,59,49,60,48,42)(38,54,56,52,46,58,55,61);(30,33)(31,38)(32,42)(34,48)(35,49)(36,51)(37,52)(39,55)(40,46)(41,58)(43,47)(44,60)(45,59)(50,56)(53,61)(54,57)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#7438, C₂₉×#7439, C₂₉×#12301, …
maximal normal subgroup of	C₂₉×#7438, C₂₉×#7439, C₂₉×#12301, …
maximal quotient of	C₂₉×#10659, C₂₉×#10660, C₂₉×#10661, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 830);