C₂₉×#2547 #16816261

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂₉×#2547

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂²×D₄×C₂₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

604 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 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)(31,33)(39,41)(40,44);(34,35,36,37)(38,39,42,41)(40,43,44,45);(30,31,32,33)(34,35)(36,37)(38,40)(39,43)(41,45)(42,44);(38,41,42,39)(40,45,44,43)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#9393, C₂₉×#9401, C₂₉×#9451, …
maximal normal subgroup of	C₂₉×#9393, C₂₉×#9401, C₂₉×#9451, …
maximal quotient of	C₂₉×#13906, C₂₉×#13911, C₂₉×#13974, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1279);

C29×#2547 #16816261