D₃×D₅×#5935 #72231106

order	11520
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂⁵

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

7968 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 7968 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:

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

maximal subgroup of	D₃×AGL(1,𝔽₅)×#5935
maximal normal subgroup of	D₃×AGL(1,𝔽₅)×#5935

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

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