C₇⋊(C₉⋊AGL(1,𝔽₅)) #11929470

order	1260
isoclinism	isoclinic class of C₇⋊(C₉⋊AGL(1,𝔽₅))
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₇⋊(C₉⋊AGL(1,𝔽₅))
unambiguous semidirect product	C₉⋊(C₇⋊AGL(1,𝔽₅))

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅×C₇×C₉	C₄
Frattini	C₃	C₃⋊(C₇⋊AGL(1,𝔽₅))
socle	C₃×C₅×C₇	Dic₃
prime radical	C₃×C₇×D₅	D₃
cosocle	C₇×C₉×D₅	C₂
LCS	G ▷ C₅×C₇×C₉
UCS	C₁

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 315

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1260, 22);