C₂₉×#2021 #16815735

order	3712
nilpotency class	3
isoclinism	isoclinic class of #2021
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₉×#2021

Subgroups

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

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

normal subgroups only

This group has 638 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) = 41
transitive degree	μ_t(G) = 464

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

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#7394, C₂₉×#12090, C₂₉×#12091, …
maximal normal subgroup of	C₂₉×#7394, C₂₉×#12090, C₂₉×#12091, …
maximal quotient of	C₂₉×#9914, C₂₉×#9915, C₂₉×#9916, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 753);