C₂₉×#3524 #16817238

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

Aliases

direct product

C₂₉×#3524

Subgroups

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

1030 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)(31,34)(35,37)(39,40)(42,50)(44,46)(48,53);(38,39,43,40)(41,46,49,44)(42,45,50,47)(48,52,53,51);(30,31)(32,35)(33,34)(36,37)(38,40,43,39)(41,46,49,44)(42,47,50,45)(48,52,53,51);(38,41,43,49)(39,44,40,46)(42,48,50,53)(45,51,47,52);(30,32,33,36)(31,35,34,37)(38,42)(39,45)(40,47)(41,48)(43,50)(44,51)(46,52)(49,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#61486, C₂₉×#61488, C₂₉×#61500, …
maximal normal subgroup of	C₂₉×#61486, C₂₉×#61488, C₂₉×#61500, …
maximal quotient of	C₂₉×#34197, C₂₉×#34237, C₂₉×#34244, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2256);

C29×#3524 #16817238