Finite Group Databasebeta

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C5×#70289 #14295916

order1920
automorphism?
homologyAbelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C22×C4

Aliases

direct productC5×#70289

Splittings

HallC3×C5 ⋊ #1764
SylowC3 ⋊ C5×#1764

Subgroups

subgroupG/H
centerC2×C4×C5D3×D4
commutatorC3×C4C2×C42×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#416C2
socleC22×C3×C5C4×D4
prime radicalC2×C3×C5×#41C22
cosocleC22×C3×C4C23×C5
hypercenterC5×#416D3
hypocenterC3C5×#1764
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C5×#416

600 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)(13,15,17,24,18,25,16,23)(14,20,21,27,22,28,19,26);(7,8)(9,10,11,12)(14,19,22,21)(20,26,28,27);(7,8)(13,14,17,21,18,22,16,19)(15,20,24,27,25,28,23,26)

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, 21614);