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C5×#80731 #14458278

order1920
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#80731

Splittings

FittingC3×C5×#466 ⋊ C2
HallC3×C5 ⋊ #3294
SylowC3 ⋊ C5×#3294

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#466C2
socleC22×C3×C5C22×D4
hypercenterC5×#466D3
hypocenterC3C5×#3294
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#466

988 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 4 generators on 24 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 183976);