C₂₉×#3521 #16817235

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

Aliases

direct product

C₂₉×#3521

Subgroups

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

1042 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)(35,37)(38,39)(40,46)(41,49)(42,43)(44,48)(45,50)(47,51)(52,53);(39,43)(44,46)(45,49)(51,52);(30,31)(32,35)(33,34)(36,37)(38,40,42,48)(39,44,43,46)(41,47,50,53)(45,51,49,52);(38,39)(40,44)(41,45)(42,43)(46,48)(47,51)(49,50)(52,53);(30,32,33,36)(31,35,34,37)(38,41)(39,45)(40,47)(42,50)(43,49)(44,51)(46,52)(48,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#61486, C₂₉×#61487, C₂₉×#61500, …
maximal normal subgroup of	C₂₉×#61486, C₂₉×#61487, C₂₉×#61500, …
maximal quotient of	C₂₉×#34195, C₂₉×#34234, C₂₉×#34237, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2253);

C29×#3521 #16817235