C₂₉×#2981 #16816695

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#2981

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂³×C₄
prime radical	C₂₉×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

402 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)(32,36)(33,35)(34,37)(38,39,42,46,41,45,49,53)(40,44,48,52,47,43,50,51);(30,32)(31,34)(33,37)(35,36)(38,40)(39,43)(41,47)(42,48)(44,45)(46,51)(49,50)(52,53);(32,37)(34,36)(38,40)(39,44)(41,47)(42,48)(43,45)(46,52)(49,50)(51,53);(31,35)(34,36)(39,45)(40,47)(46,53)(48,50)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#9279, C₂₉×#9281, C₂₉×#9283, …
maximal normal subgroup of	C₂₉×#9279, C₂₉×#9281, C₂₉×#9283, …
maximal quotient of	C₂₉×#20531, C₂₉×#20537, C₂₉×#20565, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1713);

C29×#2981 #16816695