C₅×C₄⋊(#126⋊C₃) #14510943

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₅×C₄⋊(#126⋊C₃)
unambiguous semidirect product	C₄⋊(C₅×#126⋊C₃)
unambiguous semidirect product	#2860⋊(C₃×C₅)
unambiguous semidirect product	(C₅×#2860)⋊C₃

Fitting, Hall	C₅×#2860 ⋊ C₃
Sylow	#2860 ⋊ C₃×C₅

252 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.

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

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 2 generators on 25 points:

(1,2,3,4,5)(6,7,8,9)(11,14,15)(12,17,24)(13,19,18)(16,22,23)(20,21,25);(7,9)(10,24,14,19)(11,25,15,23)(12,17,20,22)(13,18,21,16)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236641);