C₂₉×#3091 #16816805

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

Aliases

direct product

C₂₉×#3091

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂²×D₄
prime radical	C₂₉×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

420 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 4 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)(32,35)(33,34)(36,37)(38,39)(40,47)(41,45)(42,50)(43,46)(44,48)(49,52)(51,53);(31,34)(35,37);(30,32,33,36)(31,35,34,37)(38,40)(39,44)(41,48)(42,51)(43,49)(45,52)(46,53)(47,50);(38,41,43,42)(39,45,46,50)(40,48,49,51)(44,52,53,47)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#9038, C₂₉×#18107, C₂₉×#18121, …
maximal normal subgroup of	C₂₉×#9038, C₂₉×#18107, C₂₉×#18121, …
maximal quotient of	C₂₉×#20699, C₂₉×#20843, C₂₉×#20908, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1823);

C29×#3091 #16816805