Finite Group Databasebeta

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C5×#70881 #14287258

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

Aliases

direct productC5×#70881

Splittings

HallC3×C5 ⋊ #1589
SylowC3 ⋊ C5×#1589

Subgroups

subgroupG/H
centerC2×C4×C5D3×D4
commutatorC2×C3×C4C22×C4×C5
FrattiniC42C22×C5×D3
FittingC3×C4×C5×D8C2
socleC22×C3×C5C4×D4
prime radicalC2×C3×C5×D8C4
cosocleC3×C42C23×C5
hypercenterC4×C5×D8D3
hypocenterC3C5×#1589
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C42×C5 ◁ C4×C5×D8

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 960

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 12956);