D₃×AGL(1,𝔽₅)×#5935 #72260191

order	23040
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂⁵

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×#5935	C₂
cosocle	C₃×D₅×#997	C₂³
LCS	G ▷ C₃×C₅×#997
UCS	C₁ ◁ C₂

At least 9046 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

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)(9,13,12,16)(10,15,14,11);(10,13)(11,15)(14,16)

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)(9,13,12,16)(10,15,14,11), (10,13)(11,15)(14,16));