C₇×D₁₉ #63174

order	266
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×D₁₉
unambiguous semidirect product	C₁₉⋊(C₂×C₇)

Fitting, socle, Hall	C₇×C₁₉ ⋊ C₂
derived, Sylow	C₁₉ ⋊ C₂×C₇

	subgroup	G/H
center, hypercenter	C₇	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₉	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₇

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 133

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3,4,5,6,7)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);(8,9,11,13,15,17,19,21,23,25,26,24,22,20,18,16,14,12,10)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(266, 2);