Finite Group Databasebeta

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C5×#84105 #14424318

order1920
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C26

Aliases

direct productC5×#84105

Splittings

HallC3×C5 ⋊ #3009
SylowC3 ⋊ C5×#3009

Subgroups

subgroupG/H
centerC22×C5C22×#67
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
Fitting, prime radicalC2×C3×C5×H(5,𝔽2)C2
socleC22×C3×C5C22×D4
hypercenterC2×C5×H(5,𝔽2)D3
hypocenterC3C5×#3009
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C5×#41 ◁ C2×C5×H(5,𝔽2)

1504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 28 points:

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

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, 150016);