C₂₉×#1926 #16815640

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₂₉×#1926

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
prime radical	C₂²×D₄×C₂₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1856

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₉×#1926, C₂₉×#21058, C₂₉×#21059, …
maximal normal subgroup of	C₂×C₂₉×#1926, C₂₉×#21058, C₂₉×#21059, …
maximal quotient of	C₂₉×#9542, C₂₉×#9546, C₂₉×#9562, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 658);

C29×#1926 #16815640