C₁₇×AΣL(1,𝔽₂₇) #13063381

order	1377
nilpotency class	3
isoclinism	isoclinic class of AΣL(1,𝔽₂₇)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₇ · Schur multiplier (H₂) = C₃

Aliases

	subgroup	G/H
center, socle	C₃×C₁₇	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃²	C₃²×C₁₇
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₇ ◁ C₃²×C₁₇ ◁ G

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 153

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21)(20,22,25)(23,26,24);(19,22,23)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1377, 7);