C₂₉×#3487 #16817201

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

Aliases

direct product

C₂₉×#3487

Subgroups

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

1536 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)(35,36)(38,46)(40,42)(44,49);(34,35,39,36)(37,42,45,40)(38,41,46,43)(44,48,49,47);(30,31)(32,33)(34,36,39,35)(37,42,45,40)(38,43,46,41)(44,48,49,47);(34,37,39,45)(35,40,36,42)(38,44,46,49)(41,47,43,48);(34,38)(35,41)(36,43)(37,44)(39,46)(40,47)(42,48)(45,49)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8464, C₂₉×#12708, C₂₉×#12714, …
maximal normal subgroup of	C₂₉×#8464, C₂₉×#12708, C₂₉×#12714, …
maximal quotient of	C₂₉×#34174, C₂₉×#34201, C₂₉×#34249, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2219);

C29×#3487 #16817201