C₂₉×#2211 #16815925

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#2211

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₉
prime radical	C₂×D₈×C₂₉	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ C₄×C₈×C₂₉ ◁ G

158 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 64 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)(31,33)(34,35)(36,44)(37,40)(38,50)(39,53)(41,46)(42,52)(43,49)(45,60)(47,64)(48,61)(51,59)(54,58)(55,62)(56,63)(57,65);(30,31,32,33)(35,40)(41,55)(42,56)(43,53)(44,60)(50,61)(57,59)(58,64);(34,36,37,45)(35,41,40,55)(38,51,48,65)(39,54,49,47)(42,58,56,64)(43,59,53,57)(44,61,60,50)(46,63,62,52)

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#2211, C₂₉×#33579, C₂₉×#33581, …
maximal normal subgroup of	C₂×C₂₉×#2211, C₂₉×#33579, C₂₉×#33581, …
maximal quotient of	C₂₉×#12419, C₂₉×#12423, C₂₉×#12429, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 943);