C₅×#82461 #14327266

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₅ · Schur multiplier (H₂) = C₂⁵

supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₅×#82461

Splittings

Hall	C₃×C₅ ⋊ #2351
Sylow	C₃ ⋊ C₅×#2351

Subgroups

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×Q₈	C₂
socle, prime radical	C₂³×C₃×C₅	C₂⁴
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₂×C₄×C₅×Q₈	D₃
hypocenter	C₃	C₅×#2351
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×Q₈

1104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 1920

A minimal faithful permutation representation — 4 generators on 24 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 52964);

C5×#82461 #14327266