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C5×#68708 #14302932

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#68708

Splittings

FittingC3×C5×H(3,ℤ/4) ⋊ C2
HallC3×C5 ⋊ #1912
SylowC3 ⋊ C5×#1912

Subgroups

subgroupG/H
centerC2×C5#4665
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×H(3,ℤ/4)C2
socleC2×C3×C5#386
prime radicalC2×C5×#235C22
cosocleC22×C3×C4C23×C5
hypercenterC5×H(3,ℤ/4)D3
hypocenterC3C5×#1912
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C5×H(3,ℤ/4)

628 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2,3,4,5)(6,7)(9,12,15,28)(10,17,19,25)(11,21,23,37)(13,27,14,26)(16,30,31,39)(18,33,29,32)(20,34,35,40)(22,38,24,36);(9,11)(10,16,19,31)(12,21)(13,22)(14,24)(15,23)(17,30,25,39)(18,20,29,35)(26,36)(27,38)(28,37)(32,40,33,34);(7,8)(9,10,14,18,15,19,13,29)(11,20,24,31,23,35,22,16)(12,25,27,33,28,17,26,32)(21,34,38,30,37,40,36,39)

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 28630);