C₂⁴×C₃⋊ΓL(1,𝔽₁₆) #72229883

order	2880
isoclinism	isoclinic class of C₃⋊ΓL(1,𝔽₁₆)
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰×C₃

Aliases

8172 conjugacy classes of subgroups; only the 2953 normal subgroups are shown.

normal subgroups only

This group has 8172 conjugacy classes of subgroups — too many to draw. Only its 2953 normal subgroups are shown.

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

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 720

A minimal faithful permutation representation — 5 generators on 19 points:

(7,8)(9,10,11)(15,16,19,17,18);(5,6)(12,13,14);(3,4);(1,2)(3,4)(5,6)(7,8)(10,11)(13,14)(16,17,18,19);(1,2)

336 conjugacy classes. The character table is too large to display.

maximal subgroup of	C₂⁴×C₃⋊D₃×AGL(1,𝔽₅), #120×C₃⋊ΓL(1,𝔽₁₆), #72260159
maximal normal subgroup of	C₂⁴×C₃⋊D₃×AGL(1,𝔽₅), #120×C₃⋊ΓL(1,𝔽₁₆), #72260159

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

gap> G := Group((7,8)(9,10,11)(15,16,19,17,18), (5,6)(12,13,14), (3,4), (1,2)(3,4)(5,6)(7,8)(10,11)(13,14)(16,17,18,19), (1,2));