C₂₉×#2051 #16815765

order	3712
nilpotency class	3
isoclinism	isoclinic class of #2018
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#2051

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
prime radical	C₂×C₂₉×AGL(1,ℤ/8)	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

282 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 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)(36,44)(37,40)(38,42)(39,43)(41,47)(45,48)(46,49);(35,40)(36,45)(37,38)(41,44)(42,43)(48,49);(31,33)(34,36,37,46,39,45,38,47)(35,41,42,48,43,49,40,44)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#2051, C₂₉×#23530, C₂₉×#23531, …
maximal normal subgroup of	C₂×C₂₉×#2051, C₂₉×#23530, C₂₉×#23531, …
maximal quotient of	C₂₉×#10456, C₂₉×#10457, C₂₉×#10460, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 783);