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C5×#69190 #14313930

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

Aliases

direct productC5×#69190

Splittings

FittingC3×C5×#357 ⋊ C2
HallC3×C5 ⋊ #2140
SylowC3 ⋊ C5×#2140

Subgroups

subgroupG/H
centerC22×C5D3×D8
commutatorC3×C8C22×C4×C5
FrattiniC2×C8C22×C5×D3
FittingC3×C5×#357C2
socleC22×C3×C5C2×D8
prime radicalC2×C5×D3×D8C2
cosocleC2×C3×C8C23×C5
hypercenterC5×#357D3
hypocenterC3C5×#2140
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C2×C5×C8 ◁ C5×#357

520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 480

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 39628);