Finite Group Databasebeta

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C5×#80319 #14471768

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

Aliases

direct productC5×#80319

Splittings

HallC3×C5 ⋊ #3361
SylowC3 ⋊ C5×#3361

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
Fitting, prime radicalC3×C5×#459C2
socleC22×C3×C5C22×D4
hypercenterC5×#459D3
hypocenterC3C5×#3361
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#459

724 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 960

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

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

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, 197466);