C₂₉×#3486 #16817200

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

Aliases

direct product

C₂₉×#3486

Subgroups

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

1492 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)(35,39)(37,45)(40,42)(43,49);(34,35,38,39)(36,42,44,40)(37,41,45,46)(43,48,49,47);(30,31)(32,33);(34,36,38,44)(35,40,39,42)(37,43,45,49)(41,47,46,48);(34,37)(35,41)(36,43)(38,45)(39,46)(40,47)(42,48)(44,49)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8455, C₂₉×#12710, C₂₉×#12712, …
maximal normal subgroup of	C₂₉×#8455, C₂₉×#12710, C₂₉×#12712, …
maximal quotient of	C₂₉×#34173, C₂₉×#34200, C₂₉×#34249, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2218);

C29×#3486 #16817200