C₂×D₉₅ #67418

order	380
isoclinism	isoclinic class of D₉₅
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₉₀
direct product	C₂×D₉₅
unambiguous semidirect product	(C₂×C₅)⋊D₁₉
unambiguous semidirect product	(C₂×C₁₉)⋊D₅

	subgroup	G/H
center, hypercenter	C₂	D₉₅
commutator, cosocle, hypocenter	C₅×C₁₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₉	C₂
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₂

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(380, 10);