C₁₃×#3861 #14274261

order	1911
isoclinism	isoclinic class of #3861
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

Fitting, socle, Hall	C₇²×C₁₃ ⋊ C₃
derived, Sylow	C₇² ⋊ C₃×C₁₃

	subgroup	G/H
center, hypercenter	C₁₃	#3861
commutator, cosocle, hypocenter	C₇²	C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₇²×C₁₃	C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₁₃

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 637

A minimal faithful permutation representation — 3 generators on 27 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,16,17)(18,20,19)(22,23,24)(25,27,26);(21,22,23,25,24,26,27);(14,15,16,18,17,19,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1911, 10);