C₂₉×#3059 #16816773

order	3712
nilpotency class	3
isoclinism	isoclinic class of #3057
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₉×#3059

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
prime radical	C₂×#41×C₂₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×#41×C₂₉ ◁ G

460 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 200 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) = 65
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 generators on 65 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)(34,35,39,43)(36,44,48,58)(37,41,49,55)(38,51,45,42)(40,52,54,47)(46,57,60,65)(50,62,59,56)(53,63,64,61);(34,36,45,52,39,48,38,47)(35,40,51,58,43,54,42,44)(37,46,59,63,49,60,50,61)(41,53,62,65,55,64,56,57);(31,33)(34,37)(35,41)(36,46)(38,50)(39,49)(40,53)(42,56)(43,55)(44,57)(45,59)(47,61)(48,60)(51,62)(52,63)(54,64)(58,65);(37,49)(41,55)(46,60)(50,59)(53,64)(56,62)(57,65)(61,63)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#11869, C₂₉×#11871, C₂₉×#13075, …
maximal normal subgroup of	C₂₉×#11869, C₂₉×#11871, C₂₉×#13075, …
maximal quotient of	C₂₉×#19188, C₂₉×#19193, C₂₉×#19199, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1791);