C₅×#82450 #14319772

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₅ · Schur multiplier (H₂) = C₂⁴×C₄

supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₅×#82450

Splittings

Hall	C₃×C₅ ⋊ #2276
Sylow	C₃ ⋊ C₅×#2276

Subgroups

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂×C₃	C₂²×C₄²×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×#2276
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×Q₈

1256 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)(17,20,21,18)(19,23,24,22);(13,15,16,14)(17,19,21,24)(18,22,20,23);(7,8)(9,10,11,12)(17,18,21,20)(19,23,24,22);(13,14,16,15)(18,20)(22,23)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45470);

C5×#82450 #14319772