C₂₉×#2896 #16816610

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₉×#2896

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂×D₄
commutator	C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂²×D₄
prime radical	C₂²×#41×C₂₉	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 928

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)(30,31,32,33)(34,35)(36,43)(37,42)(38,46)(39,41)(40,44)(45,49)(47,48);(34,36)(35,40)(37,44)(38,47)(39,45)(41,48)(42,49)(43,46);(35,41)(40,48)(42,46)(43,49);(34,37,39,38)(35,42,41,46)(36,44,45,47)(40,49,48,43)

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#10772, C₂₉×#10778, C₂₉×#10782, …
maximal normal subgroup of	C₂₉×#10772, C₂₉×#10778, C₂₉×#10782, …
maximal quotient of	C₂₉×#17437, C₂₉×#17447, C₂₉×#17450, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1628);

C29×#2896 #16816610