C₂₉×#1630 #16815344

order	3712
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#1630

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₂₉
prime radical	C₂₉×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ G

218 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 53
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 generators on 53 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)(31,34)(32,36)(35,37)(38,39,43,46)(40,47,49,52)(41,45,42,50)(44,51,53,48);(32,36)(34,37)(38,40)(39,44)(41,48)(42,51)(43,49)(45,52)(46,53)(47,50);(30,31)(32,37)(33,35)(34,36)(38,41,43,42)(39,45,46,50)(40,48,49,51)(44,52,53,47)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#7518, C₂₉×#13676, C₂×C₂₉×#1630, …
maximal normal subgroup of	C₂₉×#7518, C₂₉×#13676, C₂×C₂₉×#1630, …
maximal quotient of	C₂₉×#7751, C₂₉×#7755, C₂₉×#7779, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 362);