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C5×#68209 #14290579

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

Aliases

direct productC5×#68209

Splittings

HallC3×C5 ⋊ #1650
SylowC3 ⋊ C5×#1650

Subgroups

subgroupG/H
centerC22×C5#882
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC5×D4⋊C8D3
hypocenterC3C5×#1650
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×D4⋊C8

400 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)(6,7,8)(9,11,13,12)(10,14,15,16)(18,24)(20,21)(23,31)(25,26)(27,32)(28,29);(7,8)(9,10)(11,14)(12,16)(13,15)(17,19,22,30)(18,23,26,32)(20,29,21,28)(24,31,25,27);(7,8)(10,14)(11,12)(15,16)(17,18,22,26)(19,27,30,31)(20,25,21,24)(23,29,32,28)

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, 16277);