Finite Group Databasebeta

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C5×#79609 #14458881

order1920
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#79609

Splittings

FittingC3×C4×C5×D8 ⋊ C2
HallC3×C5 ⋊ #3297
SylowC3 ⋊ C5×#3297

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C4×C5×D8C2
socleC22×C3×C5C22×D4
hypercenterC4×C5×D8D3
hypocenterC3C5×#3297
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C4×C5×D8

840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 4 generators on 32 points:

(1,2,3,4,5)(6,7)(11,16)(13,15);(18,23)(21,28)(22,29)(24,25)(27,32)(30,31);(7,8)(9,11)(10,13)(12,16)(14,15)(17,19,20,26)(18,22,24,30)(21,27,28,32)(23,29,25,31);(7,8)(9,10,12,14)(11,15,16,13)(17,18,20,24)(19,22,26,30)(21,23,28,25)(27,29,32,31)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 184579);