C₂₉×#1733 #16815447

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#1733

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂×D₄
commutator	C₄	C₂×C₄²×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₂₉	D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(36,42)(37,45)(38,41)(39,44)(40,46)(43,48)(47,49);(34,36)(35,39,41,47)(37,44)(38,43)(40,42,45,48)(46,49);(36,43)(39,47)(42,48)(44,49)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#10740, C₂₉×#10741, C₂₉×#10743, …
maximal normal subgroup of	C₂₉×#10740, C₂₉×#10741, C₂₉×#10743, …
maximal quotient of	C₂₉×#7866, C₂₉×#7868, C₂₉×#7869, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 465);

C29×#1733 #16815447