C₈×#41×C₂₃ #15670583

order	2944
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₈×#41×C₂₃

Subgroups

	subgroup	G/H
center	C₄×C₈×C₂₃	C₂²
commutator	C₂	C₂³×C₈×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂³×C₄
prime radical	C₂×#41×C₂₃	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₂₃ ◁ G

456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 generators on 39 points:

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

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₈×C₂₃×#104, C₂₃×#8191, C₂₃×#8192, …
maximal normal subgroup of	C₈×C₂₃×#104, C₂₃×#8191, C₂₃×#8192, …
maximal quotient of	C₈×C₂₃×#117, C₄×C₈×D₄×C₂₃, C₄×C₈×Q₈×C₂₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1696);

C8×#41×C23 #15670583