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C₄×C₂₃×AGL(1,ℤ/8) #15670563

order	2944
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

C₄×C₂₃×AGL(1,ℤ/8)

Subgroups

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

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 4 generators on 35 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);(5,6)(7,9)(8,10)(11,12);(6,9)(7,12)(10,11);(6,10)(9,11)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8954, C₂₃×#8956, C₂₃×#9095, …
maximal normal subgroup of	C₂₃×#8954, C₂₃×#8956, C₂₃×#9095, …
maximal quotient of	C₈×C₂₃×AGL(1,ℤ/8), C₂₃×#17869, C₂₃×#17871, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1676);