C₂₉×#2906 #16816620

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₉×#2906

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	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 1856

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8902, C₂₉×#8904, C₂₉×#8993, …
maximal normal subgroup of	C₂₉×#8902, C₂₉×#8904, C₂₉×#8993, …
maximal quotient of	C₂₉×#17826, C₂₉×#17827, C₂₉×#17828, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1638);

C29×#2906 #16816620