C₃×#3862 #89210

order	441
isoclinism	isoclinic class of #3862
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₃×C₇

Aliases

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

	subgroup	G/H
center, hypercenter	C₃	#3862
commutator, cosocle, hypocenter	C₇²	C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇²	C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃

28 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 63

A minimal faithful permutation representation — 2 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(441, 12);