D₃×D₅×#5934 #72278286

order	11520
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂⁶

Aliases

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

11058 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 11058 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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

maximal subgroup of	D₃×AGL(1,𝔽₅)×#5934
maximal normal subgroup of	D₃×AGL(1,𝔽₅)×#5934

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