C₁₃×#997 #11929267

order	1248
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

Fitting, Hall	C₁₃×H(5,𝔽₂) ⋊ C₃
derived, Sylow	H(5,𝔽₂) ⋊ C₃×C₁₃

	subgroup	G/H
center, socle, hypercenter	C₂×C₁₃	C₂²⋊A₄
commutator, cosocle, hypocenter	H(5,𝔽₂)	C₃×C₁₃
Frattini	C₂	C₁₃×C₂²⋊A₄
Fitting	C₁₃×H(5,𝔽₂)	C₃
LCS	G ▷ H(5,𝔽₂)
UCS	C₁ ◁ C₂×C₁₃

92 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 104

A minimal faithful permutation representation — 3 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 1379);