Finite Group Databasebeta

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C5×#68694 #14300230

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#68694

Splittings

FittingC3×C5×#336 ⋊ C2
HallC3×C5 ⋊ #1866
SylowC3 ⋊ C5×#1866

Subgroups

subgroupG/H
centerC2×C4×C5C2×D12
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#336C2
socleC22×C3×C5C4×D4
prime radicalC2×C5×#235C22
cosocleC22×C3×C4C23×C5
hypercenterC5×#336D3
hypocenterC3C5×#1866
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C5×C8 ◁ C5×#336

540 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)(13,16)(14,19)(15,24)(17,21)(18,22)(20,27)(23,25)(26,28);(7,8)(10,12)(13,15,18,25,19,27,17,26)(14,20,21,28,16,24,22,23);(7,8)(9,10)(11,12)(13,14,18,21,19,16,17,22)(15,23,25,20,27,28,26,24)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 25928);