C₂₉×#2990 #16816704

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#2990

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂³×C₄
prime radical	C₂×#41×C₂₉	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 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)(31,34)(32,36)(38,39,42,44,41,43,40,45);(30,31)(32,35)(33,34)(36,37)(39,43)(44,45);(31,34)(35,37);(30,32,33,36)(31,35,34,37)(38,40,41,42)(39,44,43,45)

Conjugacy classes & character table

1450 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#8898, C₂₉×#8900, C₂₉×#8969, …
maximal normal subgroup of	C₂₉×#8898, C₂₉×#8900, C₂₉×#8969, …
maximal quotient of	C₂₉×#20546, C₂₉×#20550, C₂₉×#20558, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1722);

C29×#2990 #16816704