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C5×#69288 #14317194

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

Aliases

direct productC5×#69288

Splittings

FittingC3×C5×C4⋊C16 ⋊ C2
HallC3×C5 ⋊ #2210
SylowC3 ⋊ C5×#2210

Subgroups

subgroupG/H
centerC22×C5C2×D24
commutator, cosocleC2×C3×C8C23×C5
FrattiniC2×C8C22×C5×D3
FittingC3×C5×C4⋊C16C2
socleC22×C3×C5C2×D8
prime radicalC2×C5×D48C2
hypercenterC5×C4⋊C16D3
hypocenterC3C5×#2210
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C4×C5×C8 ◁ C5×C4⋊C16

340 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 28 points:

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

Conjugacy classes & character table

345 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 42892);