Finite Group Databasebeta

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C5×#78759 #14458599

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

Aliases

direct productC5×#78759

Splittings

FittingC2×C3×C5×#102 ⋊ C2
HallC3×C5 ⋊ #3296
SylowC3 ⋊ C5×#3296

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC2×C3×C5×#102C2
socleC22×C3×C5C22×D4
prime radicalC5×#5806C2
hypercenterC2×C5×#102D3
hypocenterC3C5×#3296
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×#102

816 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)(6,7,8)(11,16)(13,15);(18,23)(20,28)(22,29)(24,25)(26,32)(30,31);(7,8)(9,11)(10,13)(12,16)(14,15)(17,19,21,27)(18,22,25,31)(20,26,28,32)(23,29,24,30);(9,10,12,14)(11,15,16,13)(17,18)(19,22)(20,23)(21,25)(24,28)(26,29)(27,31)(30,32)

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, 184297);