C₂×#3861 #64427

order	294
isoclinism	isoclinic class of #3861
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

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

	subgroup	G/H
center, hypercenter	C₂	#3861
commutator, cosocle, hypocenter	C₇²	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇²	C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 98

A minimal faithful permutation representation — 3 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(294, 16);