C₂₉×#2846 #16816560

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

Aliases

direct product

C₂₉×#2846

Subgroups

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

3422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 464

A minimal faithful permutation representation — 4 generators on 41 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)(31,33)(35,37)(39,41);(34,35)(36,37);(38,39)(40,41);(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#23900, C₂₉×#23984, C₂₉×#34980, …
maximal normal subgroup of	C₂₉×#23900, C₂₉×#23984, C₂₉×#34980, …
maximal quotient of	C₂₉×#14679, C₂₉×#14693, C₂₉×#14694, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1578);

C29×#2846 #16816560