C₂₉×#2229 #16815943

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₉×#2229

Subgroups

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

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

normal subgroups only

This group has 124 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) = 69
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 3 generators on 69 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)(30,31,33,35)(32,36,37,34)(38,39,41,44)(40,48,49,66)(42,54,52,67)(43,57,53,47)(45,61,59,50)(46,63,60,56)(51,68,58,64)(55,65,69,62);(30,32,33,37)(31,34,35,36)(39,44)(45,59)(46,60)(47,57)(48,66)(54,67)(62,65)(64,68);(38,40,41,49)(39,45,44,59)(42,55,52,69)(43,58,53,51)(46,64,60,68)(47,65,57,62)(48,67,66,54)(50,63,61,56)

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#2229, C₂₉×#33626, C₂₉×#33628, …
maximal normal subgroup of	C₂×C₂₉×#2229, C₂₉×#33626, C₂₉×#33628, …
maximal quotient of	C₂₉×#12814, C₂₉×#12936, C₂₉×#12938, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 961);