C₂₉×#3550 #16817264

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

Aliases

direct product

C₂₉×#3550

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
prime radical	C₂₉×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ G

1002 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)(32,36)(38,39,43,41)(40,46,48,44)(42,49,50,45)(47,51,53,52);(31,34)(35,37)(38,40,43,48)(39,44,41,46)(42,47,50,53)(45,51,49,52);(30,31,33,34)(32,35,36,37);(30,32)(31,35)(33,36)(34,37)(38,41,43,39)(40,44,48,46)(42,49,50,45)(47,51,53,52);(38,42,43,50)(39,45,41,49)(40,47,48,53)(44,51,46,52)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8492, C₂₉×#8496, C₂₉×#8531, …
maximal normal subgroup of	C₂₉×#8492, C₂₉×#8496, C₂₉×#8531, …
maximal quotient of	C₂₉×#34368, C₂₉×#34374, C₂₉×#34413, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2282);

C29×#3550 #16817264