C₂₉×#3500 #16817214

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

Aliases

direct product

C₂₉×#3500

Subgroups

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

1540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 5 generators on 49 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)(36,42)(37,45)(38,39)(40,44)(41,46)(43,47)(48,49);(35,39)(40,42)(41,45)(47,48);(30,31,32,33)(34,36)(35,40)(37,43)(38,44)(39,42)(41,47)(45,48)(46,49);(34,35)(36,40)(37,41)(38,39)(42,44)(43,47)(45,46)(48,49);(34,37,38,46)(35,41,39,45)(36,43,44,49)(40,47,42,48)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8475, C₂₉×#12715, C₂₉×#12716, …
maximal normal subgroup of	C₂₉×#8475, C₂₉×#12715, C₂₉×#12716, …
maximal quotient of	C₂₉×#34184, C₂₉×#34208, C₂₉×#34211, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2232);

C29×#3500 #16817214