Finite Group Databasebeta

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C5×#68929 #14298913

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

Aliases

direct productC5×#68929

Splittings

HallC3×C5 ⋊ #1838
SylowC3 ⋊ C5×#1838

Subgroups

subgroupG/H
centerC2×C4×C5D3×D4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#341C2
socleC22×C3×C5C2×C4⋊C4
prime radicalC23×C3×C5C2×Q8
cosocleC22×C3×C4C23×C5
hypercenterC5×#341D3
hypocenterC3C5×#1838
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C5×#341

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2,3,4,5)(6,7,8)(10,14)(13,16)(17,20,21,30,23,29,22,19)(18,25,26,24,27,28,31,32);(7,8)(9,11,12,15)(10,13,14,16)(17,19,21,20,23,30,22,29)(18,24,26,28,27,32,31,25);(9,10)(11,13)(12,14)(15,16)(17,18,22,26,23,27,21,31)(19,28,29,32,30,25,20,24)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 24611);