C₂₉×#2253 #16815967

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₉×#2253

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

116 conjugacy classes of subgroups.

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

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7452, C₂₉×#7454, C₂₉×#12463, …
maximal normal subgroup of	C₂₉×#7452, C₂₉×#7454, C₂₉×#12463, …
maximal quotient of	C₂₉×#12907, C₂₉×#13165, C₂₉×#13166, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 985);

C29×#2253 #16815967