D₅×D₁₉ #67415

order	380
isoclinism	isoclinic class of D₅×D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₅×D₁₉
unambiguous semidirect product	(D₅×C₁₉)⋊C₂
unambiguous semidirect product	(C₅×D₁₉)⋊C₂
unambiguous semidirect product	D₉₅⋊C₂

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

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 95

A minimal faithful permutation representation — 2 generators on 24 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(380, 7);