C₂₉×#1839 #16815553

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#1839

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₂₉	C₂³
commutator	C₂²	C₂²×C₈×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
socle, prime radical	C₂³×C₂₉	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₉ ◁ G

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 3 generators on 53 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)(32,37)(33,35)(34,36)(38,39)(40,42)(41,43)(44,45)(46,47,48,50,49,51,52,53);(30,32,34,33)(31,35,36,37)(38,40,41,44)(39,42,43,45);(30,33,34,32)(31,35,36,37)(39,43)(42,45)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7019, C₂₉×#7023, C₂₉×#7041, …
maximal normal subgroup of	C₂₉×#7019, C₂₉×#7023, C₂₉×#7041, …
maximal quotient of	C₂₉×#8800, C₂₉×#8801, C₂₉×#10795, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 571);

C29×#1839 #16815553