C₂₉×#3002 #16816716

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₉×#3002

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

764 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 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)(30,31)(32,33)(34,35)(36,43)(37,41)(38,46)(39,42)(40,44)(45,48)(47,49);(34,36)(35,40)(37,44)(38,47)(39,45)(41,48)(42,49)(43,46);(31,33);(34,37,39,38)(35,41,42,46)(36,44,45,47)(40,48,49,43)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#9037, C₂₉×#18100, C₂₉×#18114, …
maximal normal subgroup of	C₂₉×#9037, C₂₉×#18100, C₂₉×#18114, …
maximal quotient of	C₂₉×#18100, C₂₉×#18107, C₂₉×#18114, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1734);

C29×#3002 #16816716