C₁₃×#1020 #11929330

order	1248
isoclinism	isoclinic class of #1020
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

Fitting, socle	C₂⁴×C₁₃ ⋊ D₃
derived	C₂²⋊A₄ ⋊ C₂×C₁₃

	subgroup	G/H
center, hypercenter	C₁₃	#1020
commutator, cosocle, hypocenter	C₂²⋊A₄	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₂⁴×C₁₃	D₃
LCS	G ▷ C₂²⋊A₄
UCS	C₁ ◁ C₁₃

112 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 1442);