C₂₉×#1736 #16815450

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₉×#1736

Subgroups

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

448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#10742, C₂₉×#10749, C₂₉×#10750, …
maximal normal subgroup of	C₂₉×#10742, C₂₉×#10749, C₂₉×#10750, …
maximal quotient of	C₂₉×#7873, C₂₉×#7876, C₂₉×#7879, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 468);

C29×#1736 #16815450