C₂₉×#1446 #16815160

order	3712
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₉×#1446

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₂₉	C₂³
commutator	C₂³	C₂²×C₄×C₂₉
Frattini, cosocle	C₂⁴	C₂³×C₂₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₉ ◁ G

736 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 3 generators on 49 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)(34,35,36,37)(39,41);(38,39)(40,41)(42,43,45,47)(44,48,49,46);(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,44,45,49)(43,46,47,48)

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7131, C₂₉×#7308, C₂₉×#8455, …
maximal normal subgroup of	C₂₉×#7131, C₂₉×#7308, C₂₉×#8455, …
maximal quotient of	C₂₉×#7557, C₂₉×#11380, C₂₉×#11381, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 178);

C29×#1446 #16815160