C₂₉×#2510 #16816224

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#2510

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂²×D₄×C₂₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 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)(32,34)(33,36)(35,37)(38,39,42,44)(40,41,45,43)(46,47,49,51)(48,52,53,50);(31,32)(35,36)(38,40,42,45)(39,43,44,41)(46,47)(48,50)(49,51)(52,53);(30,32,34,31)(33,36,37,35)(38,40)(39,41)(42,45)(43,44)(46,48,49,53)(47,50,51,52);(30,33)(31,35)(32,36)(34,37)(38,41)(39,40)(42,43)(44,45)(46,47)(48,50)(49,51)(52,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₉×#2510, C₂₉×#34754, C₂₉×#34788, …
maximal normal subgroup of	C₂×C₂₉×#2510, C₂₉×#34754, C₂₉×#34788, …
maximal quotient of	C₂₉×#13883, C₂₉×#13901, C₂₉×#13999, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1242);

C29×#2510 #16816224