C₂×D₉₁ #67249

order	364
isoclinism	isoclinic class of D₉₁
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₈₂
direct product	C₂×D₉₁
unambiguous semidirect product	(C₂×C₇)⋊D₁₃
unambiguous semidirect product	(C₂×C₁₃)⋊D₇

	subgroup	G/H
center, hypercenter	C₂	D₉₁
commutator, cosocle, hypocenter	C₇×C₁₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₃	C₂
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 182

A minimal faithful permutation representation — 2 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(364, 10);