C₅×#71635 #14307086

order	1920
isoclinism	isoclinic class of #4656
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂³

supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₅×#71635

Splittings

Hall	C₃×C₅ ⋊ #1985
Sylow	C₃ ⋊ C₅×#1985

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×Q₈	C₂
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₄×C₅×Q₈	D₃
hypocenter	C₃	C₅×#1985
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₄×C₅×Q₈

560 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)(6,7,8)(13,15,16,20)(14,17,18,19)(21,24,26,25)(22,27,28,23);(7,8)(10,12)(21,23,24,28,26,27,25,22);(7,8)(9,10,11,12)(13,14,16,18)(15,19,20,17)(21,22,25,27,26,28,24,23)

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, 32784);

C5×#71635 #14307086