C₅×#1843⋊C₃ #14510690

order	1920
isoclinism	isoclinic class of #392⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₅ · Schur multiplier (H₂) = C₂

solvable

Aliases

direct product	C₅×#1843⋊C₃
unambiguous semidirect product	#1843⋊(C₃×C₅)
unambiguous semidirect product	(C₅×#1843)⋊C₃

Splittings

Fitting, Hall	C₅×#1843 ⋊ C₃
Sylow	#1843 ⋊ C₃×C₅

Subgroups

	subgroup	G/H
center, hypercenter	C₄×C₅	#127⋊C₃
commutator, hypocenter	#95	C₃×C₄×C₅
Frattini	C₂²×C₄	C₂×C₅×A₄
Fitting	C₅×#1843	C₃
socle	C₂³×C₅	C₄×A₄
prime radical	C₅×#95⋊C₃	C₄
cosocle	#376	C₂×C₃×C₅
LCS	G ▷ #95
UCS	C₁ ◁ C₄×C₅

122 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 26 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) = 49
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 2 generators on 49 points:

(1,2,3,4,5)(6,7,15,9,10,11)(8,12,17)(13,14,16)(18,19,24,35,23,28,20,25)(21,40,30,46,32,27,29,48,34,26,45,39,33,41,37,38,31,43,36,49,22,42,44,47);(6,13,9,8)(7,14,10,12)(18,32,23,31)(19,41,28,40)(20,45,24,44)(21,34,33,22)(25,49,35,48)(26,43,42,27)(29,37,36,30)(38,47,46,39)

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236388);