C₂₉×#2314 #16816028

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₉×#2314

Subgroups

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

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 1856

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#20744, C₂₉×#20745, C₂₉×#20746, …
maximal normal subgroup of	C₂₉×#20744, C₂₉×#20745, C₂₉×#20746, …
maximal quotient of	C₂₉×#13777, C₂₉×#13779, C₂₉×#13787, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1046);

C29×#2314 #16816028