C₂₉×#3496 #16817210

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

Aliases

direct product

C₂₉×#3496

Subgroups

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

1660 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 5 generators on 41 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)(31,33)(34,35)(36,40)(37,38)(39,41);(35,38)(39,40);(30,31,32,33);(34,35)(36,39)(37,38)(40,41);(34,36)(35,39)(37,41)(38,40)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8350, C₂₉×#8353, C₂₉×#8428, …
maximal normal subgroup of	C₂₉×#8350, C₂₉×#8353, C₂₉×#8428, …
maximal quotient of	C₂₉×#34181, C₂₉×#34205, C₂₉×#34206, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2228);

C29×#3496 #16817210