C₂₉×#1745 #16815459

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₂₉×#1745

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₂₉	C₂³
commutator	C₂²	C₂×C₄²×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
socle, prime radical	C₂³×C₂₉	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₉ ◁ G

272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 3 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)(34,35)(36,39)(37,38)(40,41)(42,43,44,47,45,46,48,49);(30,31,32,33)(35,38)(39,41);(34,36,37,40)(35,39,38,41)(43,46)(47,49)

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7023, C₂₉×#7043, C₂₉×#7048, …
maximal normal subgroup of	C₂₉×#7023, C₂₉×#7043, C₂₉×#7048, …
maximal quotient of	C₂₉×#8132, C₂₉×#8134, C₂₉×#8136, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 477);

C29×#1745 #16815459