C₂₉×#2452 #16816166

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₉×#2452

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

620 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)(31,32)(38,39,41,43)(40,44,45,42);(30,31,33,32)(35,37)(38,39)(40,42)(41,43)(44,45);(30,31,33,32)(34,35)(36,37);(30,32,33,31)(38,40,41,45)(39,42,43,44)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#26368, C₂₉×#26373, C₂₉×#26377, …
maximal normal subgroup of	C₂₉×#26368, C₂₉×#26373, C₂₉×#26377, …
maximal quotient of	C₂₉×#13884, C₂₉×#13920, C₂₉×#13977, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1184);

C29×#2452 #16816166