C₂₉×#2956 #16816670

order	3712
nilpotency class	3
isoclinism	isoclinic class of #576
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₉×#2956

Subgroups

	subgroup	G/H
center	C₄×C₂₉	C₂²×D₄
commutator	C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
socle	C₂×C₂₉	C₂×C₄×D₄
prime radical	C₂₉×#575	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₉ ◁ C₂×M₁₆×C₂₉ ◁ G

458 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 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)(30,31,34,38,35,32,39,37)(33,36,42,44,41,40,45,43);(30,32)(31,35)(33,40)(34,37)(36,41)(38,39)(42,43)(44,45);(30,33,34,42,35,41,39,45)(31,36,38,44,32,40,37,43);(33,41)(36,40)(42,45)(43,44)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#11669, C₂₉×#11670, C₂₉×#22898, …
maximal normal subgroup of	C₂₉×#11669, C₂₉×#11670, C₂₉×#22898, …
maximal quotient of	C₂₉×#17852, C₂₉×#17853, C₂₉×#17873, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1688);

C29×#2956 #16816670