C₂₉×#3518 #16817232

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

Aliases

direct product

C₂₉×#3518

Subgroups

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

1010 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)(38,39,44,42)(40,47,41,45)(43,50,51,46)(48,52,49,53);(38,40,44,41)(39,45,42,47)(43,48,51,49)(46,52,50,53);(30,31)(32,35)(33,34)(36,37)(38,41,44,40)(39,45,42,47)(43,49,51,48)(46,52,50,53);(38,42,44,39)(40,45,41,47)(43,50,51,46)(48,52,49,53);(30,32,33,36)(31,35,34,37)(38,43)(39,46)(40,48)(41,49)(42,50)(44,51)(45,52)(47,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8413, C₂₉×#17654, C₂₉×#17683, …
maximal normal subgroup of	C₂₉×#8413, C₂₉×#17654, C₂₉×#17683, …
maximal quotient of	C₂₉×#34193, C₂₉×#34231, C₂₉×#34242, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2250);

C29×#3518 #16817232