C₅×#86980 #14484774

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₅ · Schur multiplier (H₂) = C₂⁸

supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₅×#86980

Splittings

Fitting	C₃×C₅×#556 ⋊ C₂
Hall	C₃×C₅ ⋊ #3480
Sylow	C₃ ⋊ C₅×#3480

Subgroups

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#556	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#556	D₃
hypocenter	C₃	C₅×#3480
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#556

2224 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 5 generators on 24 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 210472);

C5×#86980 #14484774