Finite Group Databasebeta

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C5×#71655 #14301663

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#71655

Splittings

HallC3×C5 ⋊ #1890
SylowC3 ⋊ C5×#1890

Subgroups

subgroupG/H
centerC22×C5#953
commutatorC23×C3C22×C4×C5
FrattiniC24C22×C5×D3
FittingC3×C5×#518C2
socleC22×C3×C5#120
prime radicalC22×C3×C5×D4C22
cosocleC24×C3C23×C5
hypercenterC5×#518D3
hypocenterC3C5×#1890
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C24×C5 ◁ C5×#518

772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 28 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 27361);