GL(3,𝔽₂)⋊C₈ #13057022

order	1344
isoclinism	isoclinic class of SO(3,𝔽₇)
automorphism	?
homology	Abelianization (H₁) = C₈ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, Frattini, Fitting, hypercenter	C₄	SO(3,𝔽₇)
commutator, hypocenter	GL(3,𝔽₂)	C₈
socle, prime radical	C₂×GL(3,𝔽₂)	C₄
cosocle	C₄×GL(3,𝔽₂)	C₂
LCS	G ▷ GL(3,𝔽₂)
UCS	C₁ ◁ C₄

65 conjugacy classes of subgroups.

μ_t(G) = 56

Permutation generators:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 6311);