C₂₉×#2509 #16816223

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#2509

Subgroups

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

380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 4 generators on 53 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)(31,34)(32,36)(38,39,42,45)(40,44,41,43)(46,47,51,49)(48,53,52,50);(30,31,33,34)(32,35,36,37)(38,40,42,41)(39,43,45,44)(46,48)(47,50)(49,53)(51,52);(30,31)(32,35)(33,34)(36,37)(38,39)(40,43)(41,44)(42,45)(46,49,51,47)(48,53,52,50);(30,32,33,36)(31,35,34,37)(38,41,42,40)(39,44,45,43)(46,50,51,53)(47,52,49,48)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#26755, C₂₉×#26759, C₂₉×#26762, …
maximal normal subgroup of	C₂₉×#26755, C₂₉×#26759, C₂₉×#26762, …
maximal quotient of	C₂₉×#13885, C₂₉×#13933, C₂₉×#14006, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1241);

C29×#2509 #16816223