C₂₉×#3507 #16817221

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

Aliases

direct product

C₂₉×#3507

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

1012 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)(32,36)(34,37)(38,39)(40,47)(41,42)(43,44)(45,50)(46,51)(48,53)(49,52);(30,31,33,35)(32,34,36,37)(39,44)(41,46)(45,47)(48,52);(30,32,33,36)(31,34,35,37)(38,40,43,50)(39,45,44,47)(41,48,46,52)(42,49,51,53);(38,41,43,46)(39,42,44,51)(40,48,50,52)(45,49,47,53);(38,42)(39,46)(40,49)(41,44)(43,51)(45,52)(47,48)(50,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8357, C₂₉×#8431, C₂₉×#8435, …
maximal normal subgroup of	C₂₉×#8357, C₂₉×#8431, C₂₉×#8435, …
maximal quotient of	C₂₉×#34187, C₂₉×#34206, C₂₉×#34213, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2239);

C29×#3507 #16817221