C₂₉×#3535 #16817249

order	3712
nilpotency class	2
isoclinism	isoclinic class of #3532
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂₉×#3535

Subgroups

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

1038 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 928

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

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#8488, C₂₉×#18226, C₂₉×#18227, …
maximal normal subgroup of	C₂₉×#8488, C₂₉×#18226, C₂₉×#18227, …
maximal quotient of	C₂₉×#34359, C₂₉×#34376, C₂₉×#34386, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2267);

C29×#3535 #16817249