C₂⁴×AΣL(1,𝔽₂₇) #13048208

order	1296
nilpotency class	3
isoclinism	isoclinic class of AΣL(1,𝔽₂₇)
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃² · Schur multiplier (H₂) = C₂⁶×C₃

Aliases

	subgroup	G/H
center, socle	C₂⁴×C₃	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃²	C₂⁴×C₃²
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂⁴×C₃² ◁ G

1340 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 4 generators on 17 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 1926);