C₂₉×#2100 #16815814

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

Aliases

direct product

C₂₉×#2100

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

214 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 100 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)(30,31,34,36)(32,37,33,35)(38,39)(40,42)(41,43)(44,45);(30,32,34,33)(31,35,36,37)(38,40,41,44)(39,42,43,45)(46,47,49,52)(48,50,53,51);(30,33,34,32)(31,35,36,37)(39,43)(42,45)(47,50)(48,53)(51,52)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#7823, C₂₉×#7824, C₂₉×#7825, …
maximal normal subgroup of	C₂₉×#7823, C₂₉×#7824, C₂₉×#7825, …
maximal quotient of	C₂₉×#10688, C₂₉×#11207, C₂₉×#11267, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 832);