C₂×#3862 #64428

order	294
isoclinism	isoclinic class of #3862
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₇

Aliases

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

	subgroup	G/H
center, hypercenter	C₂	#3862
commutator, cosocle, hypocenter	C₇²	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇²	C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 42

A minimal faithful permutation representation — 2 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(294, 17);