C₅×#2658⋊C₃ #14510922

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

solvable

Aliases

direct product	C₅×#2658⋊C₃
unambiguous semidirect product	#2658⋊(C₃×C₅)
unambiguous semidirect product	(C₅×#2658)⋊C₃

Splittings

Fitting, Hall	C₅×#2658 ⋊ C₃
Sylow	#2658 ⋊ C₃×C₅

Subgroups

	subgroup	G/H
center	C₂×C₅	C₂×#127⋊C₃
commutator, cosocle, hypocenter	#95	C₂²×C₃×C₅
Frattini	C₂³	C₂²×C₅×A₄
Fitting	C₅×#2658	C₃
socle	C₂³×C₅	C₂²×A₄
hypercenter	C₄×C₅	#127⋊C₃
LCS	G ▷ #95
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅

274 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.

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

Full subgroup data →

Presentation

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 2 generators on 33 points:

(1,2,3,4,5)(6,7,15,9,10,11)(8,14,17,13,12,16)(18,19,22,23)(20,25,26,30,21,33,27,31,28,24,29,32);(6,8)(9,13)(11,17)(12,14)(15,16)(18,26,22,28)(19,33,23,32)(20,29,27,21)(24,25,30,31)

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236620);