C₅×#86571 #14481798

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₅ · Schur multiplier (H₂) = C₂⁸

supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₅×#86571

Splittings

Hall	C₃×C₅ ⋊ #3458
Sylow	C₃ ⋊ C₅×#3458

Subgroups

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#543	C₂
socle	C₂²×C₃×C₅	C₂⁵
prime radical	C₂⁴×C₃×C₅	C₂³
hypercenter	C₅×#543	D₃
hypocenter	C₃	C₅×#3458
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#543

1992 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 5 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 207496);

C5×#86571 #14481798