order	196
isoclinism	isoclinic class of C₇⋊D₇
automorphism	Aut(G) order 197568
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂×C₇

Aliases

direct product	C₂×C₇⋊D₇
unambiguous semidirect product	(C₂×C₇)⋊D₇

Splittings

Fitting, socle	C₂×C₇² ⋊ C₂
derived, Sylow	C₇² ⋊ C₂²

	subgroup	G/H
center, hypercenter	C₂	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₇²	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂

50 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)(8,9)(11,12)(13,14)(15,16);(1,2)(3,4,6,8,9,7,5);(10,11,13,15,16,14,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(196, 11);