C₂₉×#2252 #16815966

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#2252

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

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 3 generators on 53 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)(39,43)(40,44)(41,47)(45,53)(46,51)(48,52)(49,50);(30,32,33,37)(31,34,35,36);(38,39,44,50,41,45,48,51,42,46,52,53,47,49,40,43)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7450, C₂₉×#7451, C₂₉×#12392, …
maximal normal subgroup of	C₂₉×#7450, C₂₉×#7451, C₂₉×#12392, …
maximal quotient of	C₂₉×#12905, C₂₉×#13165, C₂₉×#13282, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 984);

C29×#2252 #16815966