C₂₉×#2064 #16815778

order	3712
nilpotency class	3
isoclinism	isoclinic class of #2018
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#2064

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
prime radical	C₂³×C₂₉	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

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

normal subgroups only

This group has 208 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) = 1856

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)(34,35,38,45,40,44,39,43)(36,42,46,41,37,48,47,49);(30,31)(32,33)(34,36,38,46,40,37,39,47)(35,41,43,42,44,49,45,48);(31,33)(34,37,40,36)(35,42,44,48)(38,46,39,47)(41,45,49,43)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#2064, C₂₉×#23601, C₂₉×#23603, …
maximal normal subgroup of	C₂×C₂₉×#2064, C₂₉×#23601, C₂₉×#23603, …
maximal quotient of	C₂₉×#10588, C₂₉×#10590, C₂₉×#10592, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 796);