C₂₉×#2062 #16815776

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

Aliases

direct product

C₂₉×#2062

Subgroups

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

314 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 928

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)(30,31,34,36)(32,37,33,35)(38,39)(40,42)(41,43)(44,45);(30,32,34,33)(31,35,36,37)(38,40)(39,42)(41,44)(43,45);(30,33,34,32)(31,35,36,37)(42,45)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#12226, C₂₉×#12227, C₂₉×#12228, …
maximal normal subgroup of	C₂₉×#12226, C₂₉×#12227, C₂₉×#12228, …
maximal quotient of	C₂₉×#10567, C₂₉×#10568, C₂₉×#10569, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 794);