C₂₉×#2361 #16816075

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₉×#2361

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#121	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

788 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 generators on 41 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)(30,31,33,32)(35,37)(38,39,41,40);(31,32)(38,40,41,39);(34,35)(36,37);(30,32,33,31)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#22855, C₂₉×#22858, C₂₉×#22863, …
maximal normal subgroup of	C₂₉×#22855, C₂₉×#22858, C₂₉×#22863, …
maximal quotient of	C₂²⋊C₄×C₄⋊C₄×C₂₉, C₂₉×#13813, C₂₉×#13820, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1093);

C29×#2361 #16816075