C₂₉×#2366 #16816080

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

Aliases

direct product

C₂₉×#2366

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#127	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

832 conjugacy classes of subgroups; only the 328 normal subgroups are shown.

normal subgroups only

This group has 832 conjugacy classes of subgroups — too many to draw. Only its 328 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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×#8920, C₂₉×#8921, C₂₉×#8924, …
maximal normal subgroup of	C₂₉×#8920, C₂₉×#8921, C₂₉×#8924, …
maximal quotient of	C₄⋊C₄²×C₂₉, C₂₉×#13820, C₂₉×#13824, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1098);