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C5×#68260 #14289388

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

Aliases

direct productC5×#68260

Splittings

FittingC3×C5×Q8⋊C8 ⋊ C2
HallC3×C5 ⋊ #1630
SylowC3 ⋊ C5×#1630

Subgroups

subgroupG/H
centerC22×C5#882
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×Q8⋊C8C2
socleC22×C3×C5#120
prime radicalC5×#874C22
hypercenterC5×Q8⋊C8D3
hypocenterC3C5×#1630
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×Q8⋊C8

436 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)(9,10)(11,16)(12,14)(13,15)(17,20,22,21)(18,24,25,29)(19,27,28,30)(23,31,32,26);(7,8)(11,15)(13,16)(17,19)(18,23)(20,27)(21,30)(22,28)(24,31)(25,32)(26,29);(7,8)(10,13)(11,15)(14,16)(17,18,22,25)(19,26,28,31)(20,24,21,29)(23,30,32,27)

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, 15086);