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C5×C3⋊#2104 #14312494

order1920
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×C3⋊#2104
unambiguous semidirect productC3⋊(C5×#2104)

Splittings

HallC3×C5 ⋊ #2104
SylowC3 ⋊ C5×#2104

Subgroups

subgroupG/H
centerC2×C5C3⋊#401
commutator, cosocleC24×C3C23×C5
FrattiniC24C22×C5×D3
FittingC3×C5×#342C2
socleC2×C3×C5#401
prime radicalC24×C3×C5C23
hypercenterC5×#342D3
hypocenterC3C5×#2104
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C24×C5 ◁ C5×#342

356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 38192);