C₈×Q₈×C₃₁ #14520626

order	1984
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₃₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₈×Q₈×C₃₁

Subgroups

	subgroup	G/H
center	C₂×C₈×C₃₁	C₂²
commutator	C₂	C₂²×C₈×C₃₁
Frattini, cosocle	C₂×C₄	C₂³×C₃₁
socle, prime radical	C₂²×C₃₁	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₃₁ ◁ G

102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 1984

A minimal faithful permutation representation — 3 generators on 47 points:

(1,2,3,4,5,6,7,8)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47);(9,10,11,12)(13,16,15,14);(9,13,11,15)(10,14,12,16)

Conjugacy classes & character table

1240 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Q₈⋊(C₃₁⋊C₁₆), C₈×#92481, C₈×#92482, …
maximal subgroup of	C₃₁×Q₈⋊C₁₆, C₈×SD₁₆×C₃₁, C₈×Q₁₆×C₃₁, …
maximal normal subgroup of	C₃₁×Q₈⋊C₁₆, C₈×SD₁₆×C₃₁, C₈×Q₁₆×C₃₁, …
maximal quotient of	C₈×C₄⋊C₄×C₃₁, C₃₁×#1916, C₃₁×#1939, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1984, 126);

C8×Q8×C31 #14520626