C₂₉×#2421 #16816135

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

Aliases

direct product

C₂₉×#2421

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

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 1856

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#24902, C₂₉×#24903, C₂₉×#24905, …
maximal normal subgroup of	C₂₉×#24902, C₂₉×#24903, C₂₉×#24905, …
maximal quotient of	C₂₉×#13875, C₂₉×#13931, C₂₉×#13969, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1153);

C29×#2421 #16816135