C₃×C₇⋊D₇ #64430

order	294
isoclinism	isoclinic class of C₇⋊D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₇

Aliases

Fitting, socle, Hall	C₃×C₇² ⋊ C₂
derived, Sylow	C₇² ⋊ C₂×C₃

	subgroup	G/H
center, hypercenter	C₃	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₇²	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃

40 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(294, 19);