C₅×#2880⋊C₃ #14510952

order	1920
isoclinism	isoclinic class of #548⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄×C₅ · Schur multiplier (H₂) = C₂²

solvable

Aliases

direct product	C₅×#2880⋊C₃
unambiguous semidirect product	#2880⋊(C₃×C₅)
unambiguous semidirect product	(C₅×#2880)⋊C₃

Splittings

Fitting, Hall	C₅×#2880 ⋊ C₃
Sylow	#2880 ⋊ C₃×C₅

Subgroups

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×A₄
commutator	C₂×Q₈	C₂×C₃×C₄×C₅
Frattini	C₂×C₄	C₂²×C₅×A₄
Fitting	C₅×#2880	C₃
socle	C₂²×C₅	C₂×C₄×A₄
prime radical	C₂²×C₅×#41⋊C₃	C₂
cosocle	C₂×#41	C₂²×C₃×C₅
hypercenter	C₅×C₂²⋊C₈	A₄
hypocenter	Q₈	C₃×C₅×C₂²⋊C₄
LCS	G ▷ C₂×Q₈ ▷ Q₈
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×C₂²⋊C₈

398 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 76 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) = 41
transitive degree	μ_t(G) = 320

A minimal faithful permutation representation — 2 generators on 41 points:

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

Conjugacy classes & character table

350 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236650);