C₂×D₉₉ #87677

order	396
isoclinism	isoclinic class of D₉₉
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₉₈
direct product	C₂×D₉₉
unambiguous semidirect product	(C₂×C₉)⋊D₁₁
unambiguous semidirect product	(C₂×C₁₁)⋊D₉

	subgroup	G/H
center, hypercenter	C₂	D₉₉
commutator, cosocle, hypocenter	C₉×C₁₁	C₂²
Frattini	C₃	C₂×D₃₃
Fitting	C₂×C₉×C₁₁	C₂
socle	C₂×C₃×C₁₁	D₃
LCS	G ▷ C₉×C₁₁
UCS	C₁ ◁ C₂

30 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 198

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(396, 9);