C₅×#69422 #14280261

order	1920
isoclinism	isoclinic class of #4656
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂⁵

supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₅×#69422

Splittings

Hall	C₃×C₅ ⋊ #1445
Sylow	C₃ ⋊ C₅×#1445

Subgroups

	subgroup	G/H
center	C₂⁴×C₅	C₂²×D₃
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂⁴	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×#95	C₂
socle, prime radical	C₂⁴×C₃×C₅	C₂³
cosocle	C₂⁴×C₃	C₂³×C₅
hypercenter	C₂×C₅×#95	D₃
hypocenter	C₃	C₅×#1445
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₅ ◁ C₂×C₅×#95

1040 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 1920

A minimal faithful permutation representation — 3 generators on 28 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 5959);

C5×#69422 #14280261