C₂₉×#3516 #16817230

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

Aliases

direct product

C₂₉×#3516

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
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)(31,34)(35,37)(39,42)(40,46)(45,49)(47,52);(38,39,43,42)(40,44,46,48)(41,49,50,45)(47,53,52,51);(30,31)(32,35)(33,34)(36,37)(38,40)(39,44)(41,47)(42,48)(43,46)(45,51)(49,53)(50,52);(38,41,43,50)(39,45,42,49)(40,47,46,52)(44,51,48,53);(30,32,33,36)(31,35,34,37)(38,42,43,39)(40,48,46,44)(41,49,50,45)(47,53,52,51)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#61472, C₂₉×#61473, C₂₉×#61490, …
maximal normal subgroup of	C₂₉×#61472, C₂₉×#61473, C₂₉×#61490, …
maximal quotient of	C₂₉×#34192, C₂₉×#34230, C₂₉×#34241, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2248);

C29×#3516 #16817230