C₂₉×#2056 #16815770

order	3712
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#2056

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

288 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 104 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) = 3712

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)(30,31)(32,33)(38,39,43,47)(40,45,49,53)(41,50,48,44)(42,52,51,46);(34,35)(36,37)(38,40,43,49)(39,44,47,50)(41,51,48,42)(45,46,53,52);(31,33)(35,37)(38,41,42,40,43,48,51,49)(39,45,46,50,47,53,52,44)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#7082, C₂₉×#7090, C₂₉×#12161, …
maximal normal subgroup of	C₂₉×#7082, C₂₉×#7090, C₂₉×#12161, …
maximal quotient of	C₂₉×#10478, C₂₉×#10479, C₂₉×#10482, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 788);