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C5×#68753 #14294478

order1920
automorphism?
homologyAbelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#68753

Splittings

FittingC3×C5×#339 ⋊ C2
HallC3×C5 ⋊ #1733
SylowC3 ⋊ C5×#1733

Subgroups

subgroupG/H
centerC2×C4×C5D3×D4
commutatorC3×C4C2×C42×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#339C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C5×D3D4
cosocleC22×C3×C4C23×C5
hypercenterC5×#339D3
hypocenterC3C5×#1733
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C5×#339

808 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 28 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20176);