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C5×#71848 #14302989

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

Aliases

direct productC5×#71848

Splittings

HallC3×C5 ⋊ #1913
SylowC3 ⋊ C5×#1913

Subgroups

subgroupG/H
centerC2×C5#5220
commutatorC23×C3C22×C4×C5
FrattiniC24C22×C5×D3
Fitting, prime radicalC3×C5×#534C2
socleC2×C3×C5#386
cosocleC24×C3C23×C5
hypercenterC5×#534D3
hypocenterC3C5×#1913
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C24×C5 ◁ C5×#534

760 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)(11,17)(13,20)(14,21)(16,19)(18,23)(22,24);(7,8)(9,11)(10,14,16,22)(12,17)(13,18)(15,21,19,24)(20,23);(7,8)(9,10)(11,14,18,22)(12,19,20,15)(13,16)(17,21)(23,24)

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, 28687);