C₂₉×#2189 #16815903

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#2189

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₉
prime radical	C₂×C₂₉×#135	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ C₂²×C₈×C₂₉ ◁ G

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

normal subgroups only

This group has 220 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) = 65
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 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)(34,35,40,44)(36,45,48,63)(37,42,39,54)(38,50,53,64)(41,56,59,47)(43,49,61,52)(46,62,55,60)(51,57,65,58);(34,36)(35,41)(37,46)(38,51)(39,55)(40,48)(42,57)(43,60)(44,59)(45,50)(47,52)(49,56)(53,65)(54,58)(61,62)(63,64);(31,33)(34,37,40,39)(35,42,44,54)(36,46,48,55)(38,49,53,52)(41,57,59,58)(43,50,61,64)(45,62,63,60)(47,51,56,65)

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#2189, C₂₉×#33516, C₂₉×#33519, …
maximal normal subgroup of	C₂×C₂₉×#2189, C₂₉×#33516, C₂₉×#33519, …
maximal quotient of	C₂₉×#12107, C₂₉×#12163, C₂₉×#12283, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 921);