C₂₉×#2029 #16815743

order	3712
nilpotency class	3
isoclinism	isoclinic class of #2021
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#2029

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#120
commutator, Frattini, cosocle	C₂⁴	C₂³×C₂₉
prime radical	C₂⁵×C₂₉	C₂²
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂⁴×C₂₉ ◁ G

466 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 45
transitive degree	μ_t(G) = 464

A minimal faithful permutation representation — 3 generators on 45 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)(30,31,33,36)(32,38,39,35)(34,37,41,43)(40,44,45,42);(30,32,33,39)(31,35,36,38)(34,40,41,45)(37,42,43,44);(35,42)(38,44)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#7426, C₂₉×#12202, C₂₉×#12203, …
maximal normal subgroup of	C₂₉×#7426, C₂₉×#12202, C₂₉×#12203, …
maximal quotient of	C₂₉×#10340, C₂₉×#10341, C₂₉×#10344, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 761);