C₅×#86294 #14480629

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₅ · Schur multiplier (H₂) = C₂⁹

supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₅×#86294

Splittings

Fitting	C₃×C₅×#534 ⋊ C₂
Hall	C₃×C₅ ⋊ #3449
Sylow	C₃ ⋊ C₅×#3449

Subgroups

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#534	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#534	D₃
hypocenter	C₃	C₅×#3449
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#534

3112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 5 generators on 28 points:

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

Conjugacy classes & character table

330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 206327);

C5×#86294 #14480629