Finite Group Databasebeta

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C5×#82509 #14430687

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

Aliases

direct productC5×#82509

Splittings

HallC3×C5 ⋊ #3080
SylowC3 ⋊ C5×#3080

Subgroups

subgroupG/H
centerC22×C5C22×#67
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C4×C5×#41C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×C5×#41C22
hypercenterC4×C5×#41D3
hypocenterC3C5×#3080
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ C4×C5×#41

768 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)(17,20,21,22)(18,25,23,26)(19,28,29,30)(24,27,31,32);(17,19)(18,24)(20,28)(21,29)(22,30)(23,31)(25,27)(26,32);(9,11,12,16)(10,13,14,15)(18,23)(24,31)(25,26)(27,32);(7,8)(9,10,12,14)(11,15,16,13)(17,18,21,23)(19,27,29,32)(20,26,22,25)(24,30,31,28)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 156385);