Finite Group Databasebeta

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C5×#71600 #14280852

order1920
automorphism?
homologyAbelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C24

Aliases

direct productC5×#71600

Splittings

HallC3×C5 ⋊ #1459
SylowC3 ⋊ C5×#1459

Subgroups

subgroupG/H
centerC2×C4×C5#217
commutatorC22×C3C22×C5×C8
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C4×C5×D4C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×C5×D4C4
cosocleC22×C3×C4C23×C5
hypercenterC2×C4×C5×D4D3
hypocenterC3C5×#1459
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C23×C4×C5 ◁ C2×C4×C5×D4

664 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 6550);