C₂₉×#3506 #16817220

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

Aliases

direct product

C₂₉×#3506

Subgroups

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

1140 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)(32,33)(34,35)(36,37)(40,44)(42,45);(31,35)(32,36)(38,39,41,43)(40,42,44,45);(38,40,41,44)(39,42,43,45);(30,32,34,36)(31,33,35,37);(30,33)(31,36)(32,35)(34,37)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8358, C₂₉×#8430, C₂₉×#8434, …
maximal normal subgroup of	C₂₉×#8358, C₂₉×#8430, C₂₉×#8434, …
maximal quotient of	C₂₉×#34186, C₂₉×#34206, C₂₉×#34213, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2238);

C29×#3506 #16817220