order	360
isoclinism	isoclinic class of D₃×ΓL(1,𝔽₁₆)
automorphism	Aut(G) = D₃²×AGL(1,𝔽₅) (order 720) · Inn(G) = G · Out(G) = C₂
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×ΓL(1,𝔽₁₆)
unambiguous semidirect product	(C₃×D₃)⋊AGL(1,𝔽₅)

Splittings

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅	C₂×C₄
prime radical	C₃×D₃×D₅	C₂
cosocle	C₃²×D₅	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁

70 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 30

A minimal faithful permutation representation — 2 generators on 11 points:

(1,2,3)(5,6)(8,9,10,11);(2,3)(4,5,6)(7,8,11,9,10)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 128);