C₂₉×#2531 #16816245

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₂₉×#2531

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

454 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)(32,36)(33,34)(35,37)(39,42)(40,44)(46,47,49,51)(48,50,52,53);(31,34)(35,36)(38,39,41,42)(40,43,44,45)(46,47,49,51)(48,50,52,53);(30,31)(32,35)(33,34)(36,37)(38,39)(40,43)(41,42)(44,45)(46,47)(48,50)(49,51)(52,53);(30,32,33,37)(31,35,34,36)(38,40)(39,43)(41,44)(42,45)(46,48,49,52)(47,50,51,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₉×#2531, C₂₉×#34797, C₂₉×#34806, …
maximal normal subgroup of	C₂×C₂₉×#2531, C₂₉×#34797, C₂₉×#34806, …
maximal quotient of	C₂₉×#13898, C₂₉×#13946, C₂₉×#14012, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1263);

C29×#2531 #16816245