Finite Group Databasebeta

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C5×#67741 #14276830

order1920
automorphism?
homologyAbelianization (H1) = C4×C5×C8 · Schur multiplier (H2) = C2×C4

Aliases

direct productC5×#67741

Splittings

HallC3×C5 ⋊ #1281
SylowC3 ⋊ C5×#1281

Subgroups

subgroupG/H
centerC2×C4×C5(C2×D3)⋊C4
commutatorC22×C3C4×C5×C8
FrattiniC2×C42C2×C5×D3
FittingC3×C5×#431C2
socleC22×C3×C5#95
prime radicalC23×C3×C5C42
cosocleC2×C3×C42C22×C5
hypercenterC5×#431D3
hypocenterC3C5×#1281
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C2×C42×C5 ◁ C5×#431

304 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 32 points:

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

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, 2528);