C₂₉×#3491 #16817205

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

Aliases

direct product

C₂₉×#3491

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
prime radical	C₂₉×#534	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ G

1052 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)(32,36)(34,37)(38,39)(40,44)(41,48)(42,43)(45,49)(46,52)(47,50)(51,53);(30,31,33,35)(32,34,36,37)(39,43)(44,50)(45,48)(51,52);(30,32)(31,34)(33,36)(35,37)(38,40,42,47)(39,44,43,50)(41,46,49,53)(45,51,48,52);(38,39)(40,44)(41,45)(42,43)(46,51)(47,50)(48,49)(52,53);(38,41)(39,45)(40,46)(42,49)(43,48)(44,51)(47,53)(50,52)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8348, C₂₉×#8540, C₂₉×#12726, …
maximal normal subgroup of	C₂₉×#8348, C₂₉×#8540, C₂₉×#12726, …
maximal quotient of	C₂₉×#34177, C₂₉×#34199, C₂₉×#34219, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2223);

C29×#3491 #16817205