C₂₉×#2946 #16816660

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×#2946

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂²×D₄
commutator	C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
prime radical	C₂×C₂₉×AGL(1,ℤ/8)	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂₉×#117 ◁ G

506 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 4 generators on 49 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)(30,31,33,32)(34,35)(36,40)(37,39)(38,42)(41,45)(43,47)(44,46)(48,49);(35,39)(37,45)(40,46)(41,42)(44,49)(47,48);(30,32,33,31)(34,36)(35,40)(37,44)(38,43)(39,46)(41,48)(42,47)(45,49);(36,43)(40,47)(44,49)(46,48)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#22891, C₂₉×#22893, C₂₉×#22895, …
maximal normal subgroup of	C₂₉×#22891, C₂₉×#22893, C₂₉×#22895, …
maximal quotient of	C₂₉×#17852, C₂₉×#17873, C₂₉×#17875, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1678);

C29×#2946 #16816660