C₅×#68606 #14298736

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×#68606

Splittings

Hall	C₃×C₅ ⋊ #1832
Sylow	C₃ ⋊ C₅×#1832

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#336	C₂
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#336	D₃
hypocenter	C₃	C₅×#1832
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₅×#336

432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 1920

A minimal faithful permutation representation — 3 generators on 36 points:

(1,2,3,4,5)(6,7,8)(9,11,12,10)(14,18)(17,20)(23,29)(26,32)(30,35)(33,36);(7,8)(9,10,12,11)(13,15,16,19)(14,17,18,20)(21,23)(22,26)(24,30)(25,29)(27,33)(28,32)(31,35)(34,36);(10,11)(13,14)(15,17)(16,18)(19,20)(21,22,24,27,25,28,31,34)(23,26,30,33,29,32,35,36)

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, 24434);

C5×#68606 #14298736