C₅×#2801⋊C₃ #14510926

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

solvable

Aliases

direct product	C₅×#2801⋊C₃
unambiguous semidirect product	#2801⋊(C₃×C₅)
unambiguous semidirect product	(C₅×#2801)⋊C₃

Splittings

Fitting, Hall	C₅×#2801 ⋊ C₃
Sylow	#2801 ⋊ C₃×C₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅	#560⋊C₃
commutator, cosocle, hypocenter	#95	C₂²×C₃×C₅
Frattini	C₂³	C₂²×C₅×A₄
Fitting	C₅×#2801	C₃
socle	C₂³×C₅	C₂²×A₄
LCS	G ▷ #95
UCS	C₁ ◁ C₂×C₅

210 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 36 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)(6,8,25)(7,14,23,11,12,21)(9,17,26,19,20,27)(10,15,16)(13,22,29)(18,24,28);(6,13,10,18)(7,9,11,19)(8,24,15,22)(12,20,14,17)(16,21)(23,25)(26,29)(27,28)

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, 236624);