C₂₉×#2505 #16816219

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

Aliases

direct product

C₂₉×#2505

Subgroups

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

456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 1856

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)(30,31,34,35)(32,37,36,33)(38,39,42,44)(40,41,45,43)(47,50)(48,52);(31,35)(32,36)(38,40,42,45)(39,43,44,41)(46,47)(48,51)(49,50)(52,53);(30,32,34,36)(31,33,35,37)(38,40)(39,41)(42,45)(43,44)(46,48,49,52)(47,51,50,53);(30,33)(31,36)(32,35)(34,37)(38,41)(39,40)(42,43)(44,45)(46,47)(48,51)(49,50)(52,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₉×#2505, C₂₉×#34754, C₂₉×#34772, …
maximal normal subgroup of	C₂×C₂₉×#2505, C₂₉×#34754, C₂₉×#34772, …
maximal quotient of	C₂₉×#13883, C₂₉×#13896, C₂₉×#14004, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1237);

C29×#2505 #16816219