C₅×C₄⋊(#127⋊C₃) #14510945

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product	C₅×C₄⋊(#127⋊C₃)
unambiguous semidirect product	C₄⋊(C₅×#127⋊C₃)
unambiguous semidirect product	#2867⋊(C₃×C₅)
unambiguous semidirect product	(C₅×#2867)⋊C₃

Fitting, Hall	C₅×#2867 ⋊ C₃
Sylow	#2867 ⋊ C₃×C₅

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

normal subgroups only

This group has 504 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) = 17
transitive degree	μ_t(G) = 60

A minimal faithful permutation representation — 2 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236643);