C₃⋊(ΓL(1,𝔽₈)⋊Dic₅) #11929495

order	1260
isoclinism	isoclinic class of C₃⋊(C₅⋊AGL(1,𝔽₇))
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₃⋊(ΓL(1,𝔽₈)⋊Dic₅)
unambiguous semidirect product	ΓL(1,𝔽₈)⋊Dic₁₅
unambiguous semidirect product	Dic₁₀₅⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊(C₅⋊AGL(1,𝔽₇))
commutator, hypocenter	C₃×C₅×C₇	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₅×C₇	C₂×C₃
prime radical	C₂×C₃×C₅×ΓL(1,𝔽₈)	C₂
LCS	G ▷ C₃×C₅×C₇
UCS	C₁ ◁ C₂

56 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 420

Polycyclic presentation:

2,3,2,3,5,7|a^2=c,d^a=d^2,e^a=e^4,f^a=f^6,f^b=f^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1260, 47);