C₂₉×#2074 #16815788

order	3712
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#2074

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

222 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 57
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 3 generators on 57 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)(36,39)(37,38)(40,41)(42,43)(44,47)(45,48)(46,49)(50,57)(51,55)(52,54)(53,56);(35,38)(39,41)(42,44,45,51)(43,47,48,55)(46,50,53,52)(49,57,56,54);(31,33)(34,36,37,40)(35,39,38,41)(43,48)(44,50)(46,53)(47,54)(51,52)(55,57)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#7413, C₂×C₂₉×#2074, C₂₉×#23627, …
maximal normal subgroup of	C₂₉×#7413, C₂×C₂₉×#2074, C₂₉×#23627, …
maximal quotient of	C₂₉×#10623, C₂₉×#10624, C₂₉×#10626, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 806);