C₇⋊AGL(1,𝔽₉) #92739

order	504
isoclinism	isoclinic class of C₇⋊AGL(1,𝔽₉)
automorphism	?
homology	Abelianization (H₁) = C₈ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₇	C₈
prime radical	C₇×C₃⋊D₃	C₄
cosocle	C₇×#157	C₂
LCS	G ▷ C₃²×C₇
UCS	C₁

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 63

A minimal faithful permutation representation — 2 generators on 16 points:

(2,4,5,7,6,8,9,3)(11,12)(13,14)(15,16);(1,9,5)(2,8,3)(4,6,7)(10,11,13,15,16,14,12)

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 165);