C₂₉×#2395 #16816109

order	3712
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#2395

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₂₉	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₉
socle	C₂³×C₂₉	C₂⁴
prime radical	C₂²×D₄×C₂₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₉ ◁ G

560 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)(36,39)(37,38)(40,41)(42,43)(44,46)(45,47)(48,49);(30,31)(32,33)(35,38)(39,41)(42,44,45,48)(43,46,47,49);(31,33)(43,47)(46,49);(34,36,37,40)(35,39,38,41)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#9011, C₂₉×#9012, C₂₉×#11727, …
maximal normal subgroup of	C₂₉×#9011, C₂₉×#9012, C₂₉×#11727, …
maximal quotient of	C₂₉×#13839, C₂₉×#13842, C₂₉×#13844, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1127);

C29×#2395 #16816109