C₂₉×#2053 #16815767

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

Aliases

direct product

C₂₉×#2053

Subgroups

	subgroup	G/H
center	C₄×C₂₉	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
socle	C₂×C₂₉	#394
prime radical	C₂₉×#575	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

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

normal subgroups only

This group has 264 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)(32,41)(33,46)(34,51)(35,39)(36,40)(37,43)(38,48)(42,52)(44,54)(45,53)(47,55)(49,56)(50,59)(57,60)(58,61);(30,32)(31,37)(33,47)(34,44)(35,43)(36,45)(38,55)(39,53)(40,54)(41,51)(42,49)(46,52)(48,58)(50,57)(56,60)(59,61);(30,33,34,48,36,50,35,49)(31,38,39,46,40,56,51,59)(32,42,43,57,45,58,44,47)(37,52,41,55,54,61,53,60)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#12170, C₂₉×#12171, C₂₉×#12172, …
maximal normal subgroup of	C₂₉×#12170, C₂₉×#12171, C₂₉×#12172, …
maximal quotient of	C₂₉×#10464, C₂₉×#10465, C₂₉×#10466, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 785);