C₇×AGL(2,𝔽₃) #72224661

order	3024
isoclinism	isoclinic class of AGL(2,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₂×C₇ · Schur multiplier (H₂) = C₁

Aliases

Fitting, socle	C₃²×C₇ ⋊ GL(2,𝔽₃)
derived	PSU(3,𝔽₂)⋊C₃ ⋊ C₂×C₇

	subgroup	G/H
center, hypercenter	C₇	AGL(2,𝔽₃)
commutator, cosocle, hypocenter	PSU(3,𝔽₂)⋊C₃	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇	GL(2,𝔽₃)
LCS	G ▷ PSU(3,𝔽₂)⋊C₃
UCS	C₁ ◁ C₇

92 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:

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

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,7,4,6,3,9,5,2)(10,11,12,13,14,15,16), (3,5,6)(7,8,9));