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C5×#83988 #14454450

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

Aliases

direct productC5×#83988

Splittings

FittingC2×C3×C5×#137 ⋊ C2
HallC3×C5 ⋊ #3269
SylowC3 ⋊ C5×#3269

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC2×C3×C5×#137C2
socleC22×C3×C5C22×D4
hypercenterC2×C5×#137D3
hypocenterC3C5×#3269
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×#137

956 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 4 generators on 28 points:

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

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, 180148);