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C5×#68365 #14284223

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

Aliases

direct productC5×#68365

Splittings

FittingC3×C5×#330 ⋊ C2
HallC3×C5 ⋊ #1531
SylowC3 ⋊ C5×#1531

Subgroups

subgroupG/H
centerC22×C5D3×C22⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#330C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C5×D3C22⋊C4
cosocleC3×C42C23×C5
hypercenterC5×#330D3
hypocenterC3C5×#1531
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#330

424 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)(7,8)(9,11,13,12)(10,14,15,16)(18,23)(22,25)(24,31)(30,32);(6,7,8)(9,10)(11,14)(12,16)(13,15)(17,19,21,27)(18,22,23,25)(20,28,29,26)(24,32,31,30);(10,14,15,16)(17,18,20,24,21,23,29,31)(19,25,26,32,27,22,28,30)

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, 9921);