C₂₉×#3512 #16817226

order	3712
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂₉×#3512

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ G

1032 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 5 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)(32,36)(34,37)(38,39)(40,45)(41,46)(42,50)(43,44)(47,51)(48,49)(52,53);(30,31,33,35)(32,34,36,37)(39,44)(41,45)(47,50)(49,52);(30,32,33,36)(31,34,35,37)(38,40,43,46)(39,45,44,41)(42,48,51,53)(47,52,50,49);(38,41,43,45)(39,46,44,40)(42,49,51,52)(47,53,50,48);(38,42,43,51)(39,47,44,50)(40,48,46,53)(41,49,45,52)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8476, C₂₉×#17687, C₂₉×#17690, …
maximal normal subgroup of	C₂₉×#8476, C₂₉×#17687, C₂₉×#17690, …
maximal quotient of	C₂₉×#34189, C₂₉×#34208, C₂₉×#34217, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2244);

C29×#3512 #16817226