C₂⁶×ΓL(1,𝔽₈) #13062421

order	1344
isoclinism	isoclinic class of ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₃ · Schur multiplier (H₂) = C₂¹⁵

Aliases

Fitting, socle, Hall	C₂⁶×C₇ ⋊ C₃
derived, Sylow	C₇ ⋊ C₂⁶×C₃

	subgroup	G/H
center, hypercenter	C₂⁶	ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇	C₂⁶×C₃
Frattini	C₁	G
Fitting, socle	C₂⁶×C₇	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₂⁶

11300 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 448

A minimal faithful permutation representation — 6 generators on 19 points:

(1,2)(14,15,16)(17,19,18);(3,4)(13,14,15,17,16,18,19);(5,6);(7,8);(9,10);(11,12)

320 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 11710);