C₂₉×#2514 #16816228

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

Aliases

direct product

C₂₉×#2514

Subgroups

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

372 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#27063, C₂₉×#27067, C₂₉×#27070, …
maximal normal subgroup of	C₂₉×#27063, C₂₉×#27067, C₂₉×#27070, …
maximal quotient of	C₂₉×#13885, C₂₉×#13921, C₂₉×#13989, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1246);

C29×#2514 #16816228