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C5×#69346 #14314622

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

Aliases

direct productC5×#69346

Splittings

FittingC3×C5×#367 ⋊ C2
HallC3×C5 ⋊ #2159
SylowC3 ⋊ C5×#2159

Subgroups

subgroupG/H
centerC22×C5D3×D8
commutatorC3×C8C22×C4×C5
FrattiniC2×C8C22×C5×D3
FittingC3×C5×#367C2
socleC22×C3×C5C2×D8
prime radicalC22×C5×D3D8
cosocleC2×C3×C8C23×C5
hypercenterC5×#367D3
hypocenterC3C5×#2159
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C2×C5×C8 ◁ C5×#367

312 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)(14,20)(18,24)(21,25)(26,28);(13,14,19,26,16,21,23,24,17,20,27,28,22,25,15,18);(7,8)(9,10,11,12)(14,18)(15,19)(16,22)(20,24)(21,28)(23,27)(25,26)

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, 40320);