C₃×#3861 #89209

order	441
isoclinism	isoclinic class of #3861
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₃

Aliases

Fitting, socle	C₃×C₇² ⋊ C₃
derived, Sylow	C₇² ⋊ C₃²

	subgroup	G/H
center, hypercenter	C₃	#3861
commutator, cosocle, hypocenter	C₇²	C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇²	C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 147

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(441, 11);