C₄×C₂₉×AGL(1,ℤ/8) #16816658

order	3712
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₄×C₂₉×AGL(1,ℤ/8)

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂×D₄
commutator	C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂²×D₄
prime radical	C₂×C₂₉×AGL(1,ℤ/8)	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 4 generators on 41 points:

(1,2,3,4)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(5,6)(7,9)(8,10)(11,12);(6,9)(7,12)(10,11);(6,10)(9,11)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8954, C₂₉×#8956, C₂₉×#9095, …
maximal normal subgroup of	C₂₉×#8954, C₂₉×#8956, C₂₉×#9095, …
maximal quotient of	C₈×C₂₉×AGL(1,ℤ/8), C₂₉×#17869, C₂₉×#17871, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1676);

C4×C29×AGL(1,ℤ/8) #16816658