C₂×C₅×D₁₉ #67416

order	380
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×D₁₉
unambiguous semidirect product	C₁₉⋊(C₂²×C₅)
unambiguous semidirect product	(C₂×C₁₉)⋊(C₂×C₅)

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₉	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₅

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 190

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);(1,2)(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(380, 8);