C₂⁴×D₁₅ #92136

order	480
isoclinism	isoclinic class of D₁₅
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂⁴×D₁₅

	subgroup	G/H
center, hypercenter	C₂⁴	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂⁵
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃×C₅	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂⁴

1496 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 5 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1212);