C₂₉×#1927 #16815641

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₉×#1927

Subgroups

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

254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 3712

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)(38,39,41,44)(40,42,45,43);(30,31,33,32)(34,36,37,35);(30,32,33,31)(39,42)(40,45)(43,44)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₉×#1927, C₂₉×#21058, C₂₉×#21059, …
maximal normal subgroup of	C₂×C₂₉×#1927, C₂₉×#21058, C₂₉×#21059, …
maximal quotient of	C₂₉×#9543, C₂₉×#9547, C₂₉×#9565, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 659);

C29×#1927 #16815641