C₂₉×#3505 #16817219

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

Aliases

direct product

C₂₉×#3505

Subgroups

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

1152 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)(40,44)(42,45);(31,34)(35,36)(38,39,41,43)(40,42,44,45);(38,40,41,44)(39,42,43,45);(30,31)(32,35)(33,34)(36,37);(30,32)(31,35)(33,37)(34,36)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8352, C₂₉×#8538, C₂₉×#17615, …
maximal normal subgroup of	C₂₉×#8352, C₂₉×#8538, C₂₉×#17615, …
maximal quotient of	C₂₉×#34185, C₂₉×#34205, C₂₉×#34212, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2237);

C29×#3505 #16817219