ΓL(1,𝔽₁₆)×#5934 #72278331

order	11520
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂	ΓL(1,𝔽₁₆)×#1020
commutator, hypocenter	C₃×C₅×#997	C₂×C₄
Fitting	C₃×C₅×H(5,𝔽₂)	C₄×D₃
socle	C₂×C₃×C₅	C₄×#1020
prime radical	C₃×D₅×#5934	C₂
cosocle	C₃×D₅×#997	C₂²
LCS	G ▷ C₃×C₅×#997
UCS	C₁ ◁ C₂

3318 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 3318 conjugacy classes of subgroups — too many to draw. Only its 62 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 — 2 generators on 16 points:

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

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