C₅×#2863⋊C₃ #14510944

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

Aliases

direct product	C₅×#2863⋊C₃
unambiguous semidirect product	#2863⋊(C₃×C₅)
unambiguous semidirect product	(C₅×#2863)⋊C₃

Splittings

Fitting, Hall	C₅×#2863 ⋊ C₃
Sylow	#2863 ⋊ C₃×C₅

Subgroups

	subgroup	G/H
center	C₂×C₅	C₂×#126⋊C₃
commutator, cosocle	C₂×C₄²	C₂²×C₃×C₅
Frattini	C₂³	C₂²×C₅×A₄
Fitting	C₅×#2863	C₃
socle	C₂³×C₅	C₂²×A₄
prime radical	C₂×C₅×C₄²⋊C₃	C₂²
hypercenter	C₄×C₅	#126⋊C₃
hypocenter	C₄²	C₃×C₅×Q₈
LCS	G ▷ C₂×C₄² ▷ C₄²
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅

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

normal subgroups only

This group has 196 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.

Full subgroup data →

Presentation

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 2 generators on 29 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236642);