C₂₉×#2865 #16816579

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#2865

Subgroups

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

418 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)(31,34)(32,36)(39,42)(40,44)(47,49)(51,52);(38,39)(40,43)(41,42)(44,45)(46,47,50,49)(48,51,53,52);(30,31,33,34)(32,35,36,37)(38,39)(40,43)(41,42)(44,45)(46,48,50,53)(47,51,49,52);(30,32)(31,35)(33,36)(34,37)(38,40,41,44)(39,43,42,45)(46,49,50,47)(48,52,53,51)

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#35027, C₂₉×#35028, C₂₉×#35040, …
maximal normal subgroup of	C₂₉×#35027, C₂₉×#35028, C₂₉×#35040, …
maximal quotient of	C₂₉×#14690, C₂₉×#14701, C₂₉×#14704, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1597);

C29×#2865 #16816579