C₂₉×#3585 #16817299

order	3712
nilpotency class	3
isoclinism	isoclinic class of #3585
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₂₉×#3585

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₉	C₂³×D₄
commutator, Frattini, cosocle	C₄	C₂⁵×C₂₉
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₂×#41×C₂₉ ◁ G

1464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 464

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

Conjugacy classes & character table

1189 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#23872, C₂₉×#23874, C₂₉×#23882, …
maximal normal subgroup of	C₂₉×#23872, C₂₉×#23874, C₂₉×#23882, …
maximal quotient of	C₂₉×#60087, C₂₉×#60089, C₂₉×#60109, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2317);

C29×#3585 #16817299