C₂³×D₁₅ #6846

order	240
isoclinism	isoclinic class of D₁₅
automorphism	Aut(G) order 161280
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂³×D₁₅

	subgroup	G/H
center, hypercenter	C₂³	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂⁴
Frattini	C₁	G
Fitting, socle	C₂³×C₃×C₅	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂³

268 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 4 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(240, 207);