C₂₉×#3519 #16817233

order	3712
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂₉×#3519

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ G

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 5 generators on 45 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)(30,31)(32,36)(33,34)(35,37)(38,39)(40,44)(41,42)(43,45);(31,34)(35,36)(39,42)(43,44);(38,40)(39,43)(41,45)(42,44);(30,31)(32,35)(33,34)(36,37)(38,39)(40,43)(41,42)(44,45);(30,32,33,37)(31,35,34,36)(38,40)(39,43)(41,45)(42,44)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8416, C₂₉×#17547, C₂₉×#17597, …
maximal normal subgroup of	C₂₉×#8416, C₂₉×#17547, C₂₉×#17597, …
maximal quotient of	C₂₉×#34194, C₂₉×#34233, C₂₉×#34236, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2251);

C29×#3519 #16817233