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C5×#80032 #14436327

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

Aliases

direct productC5×#80032

Splittings

HallC3×C5 ⋊ #3121
SylowC3 ⋊ C5×#3121

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#448C2
socleC22×C3×C5C22×D4
prime radicalC3×C5×#121C22
hypercenterC5×#448D3
hypocenterC3C5×#3121
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#448

740 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 4 generators on 32 points:

(1,2,3,4,5)(7,8)(9,11,12,15)(10,14,13,16)(18,23)(22,30)(24,31)(29,32);(6,7,8)(17,19,21,26)(18,22,23,30)(20,28,27,25)(24,32,31,29);(10,13)(14,16)(17,18)(19,22)(20,24)(21,23)(25,29)(26,30)(27,31)(28,32);(9,10)(11,14)(12,13)(15,16)(19,25)(20,27)(22,29)(24,31)(26,28)(30,32)

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, 162025);