C₂²×C₂₉×AGL(1,ℤ/8) #16817292

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

Aliases

direct product

C₂²×C₂₉×AGL(1,ℤ/8)

Subgroups

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

1720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 5 generators on 41 points:

(1,2)(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);(3,4);(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×#11012, C₂₉×#11014, C₂₉×#11016, …
maximal normal subgroup of	C₂₉×#11012, C₂₉×#11014, C₂₉×#11016, …
maximal quotient of	C₂²×C₂₉×#418, C₂²×C₂₉×#417, C₂²×C₂₉×#428, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2310);

C22×C29×AGL(1,ℤ/8) #16817292