C₂²×D₄₅ #67119

order	360
isoclinism	isoclinic class of D₄₅
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

C₂²×D₄₅

	subgroup	G/H
center, hypercenter	C₂²	D₄₅
commutator, cosocle, hypocenter	C₅×C₉	C₂³
Frattini	C₃	C₂²×D₁₅
Fitting	C₂²×C₅×C₉	C₂
socle	C₂²×C₃×C₅	D₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₂²

96 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 180

A minimal faithful permutation representation — 3 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 49);