D₃×AGL(1,𝔽₅)×#5934 #72278578

order	23040
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×AGL(1,𝔽₅)×#1020
commutator, hypocenter	C₃×C₅×#997	C₂²×C₄
Fitting	C₃×C₅×H(5,𝔽₂)	C₂×C₄×D₃
socle	C₂×C₃×C₅	C₂×C₄×#1020
prime radical	D₃×D₅×#5934	C₂
cosocle	C₃×D₅×#997	C₂³
LCS	G ▷ C₃×C₅×#997
UCS	C₁ ◁ C₂

20966 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 3 generators on 16 points:

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

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2,3)(5,6,7,8)(10,15,13)(11,16,14), (2,3)(4,5,8,6,7)(9,10)(11,13)(12,14)(15,16), (10,11)(14,15));