C₂₉×#2478 #16816192

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

Aliases

direct product

C₂₉×#2478

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

476 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)(35,36)(37,41)(42,43)(44,45)(46,48)(47,49);(31,33)(34,35,38,36)(37,39,41,40)(42,44,46,49)(43,45,48,47);(30,31)(32,33)(34,36,38,35)(37,40,41,39)(42,44)(43,47)(45,48)(46,49);(34,37)(35,39)(36,40)(38,41)(42,45,46,47)(43,44,48,49)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₉×#2478, C₂₉×#34724, C₂₉×#34735, …
maximal normal subgroup of	C₂×C₂₉×#2478, C₂₉×#34724, C₂₉×#34735, …
maximal quotient of	C₂₉×#13900, C₂₉×#13943, C₂₉×#13989, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1210);

C29×#2478 #16816192