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C5×#68417 #14284577

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#68417

Splittings

FittingC3×C5×#332 ⋊ C2
HallC3×C5 ⋊ #1540
SylowC3 ⋊ C5×#1540

Subgroups

subgroupG/H
centerC22×C5D3×C22⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#332C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5725C2
cosocleC3×C42C23×C5
hypercenterC5×#332D3
hypocenterC3C5×#1540
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#332

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 32 points:

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

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, 10275);