C₂₉×#3547 #16817261

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

Aliases

direct product

C₂₉×#3547

Subgroups

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

1022 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)(38,39,42,43)(40,46,47,44)(41,49,50,45)(48,51,53,52);(31,34)(35,37)(39,43)(40,47)(45,49)(48,53);(30,31,33,34)(32,35,36,37)(38,40,42,47)(39,44,43,46)(41,48,50,53)(45,51,49,52);(30,32)(31,35)(33,36)(34,37)(38,39)(40,44)(41,45)(42,43)(46,47)(48,51)(49,50)(52,53);(38,41,42,50)(39,45,43,49)(40,48,47,53)(44,51,46,52)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8502, C₂₉×#18706, C₂₉×#18707, …
maximal normal subgroup of	C₂₉×#8502, C₂₉×#18706, C₂₉×#18707, …
maximal quotient of	C₂₉×#34367, C₂₉×#34383, C₂₉×#34394, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2279);

C29×#3547 #16817261