C₁₃×#1113 #13064083

order	1404
isoclinism	isoclinic class of #1113
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

Fitting, socle, Hall	C₃³×C₁₃ ⋊ C₂²
derived, Sylow	C₃³ ⋊ C₂²×C₁₃

	subgroup	G/H
center, hypercenter	C₁₃	#1113
commutator, cosocle, hypocenter	C₃³	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃³×C₁₃	C₂²
LCS	G ▷ C₃³
UCS	C₁ ◁ C₁₃

108 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 156

A minimal faithful permutation representation — 2 generators on 22 points:

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

maximal subgroup of	D₁₃×#1113
maximal normal subgroup of	D₁₃×#1113

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1404, 215);