Finite Group Databasebeta

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C5×#83652 #14460090

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

Aliases

direct productC5×#83652

Splittings

FittingC3×C5×#555 ⋊ C2
HallC3×C5 ⋊ #3303
SylowC3 ⋊ C5×#3303

Subgroups

subgroupG/H
centerC22×C5C22×#67
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#555C2
socleC22×C3×C5C22×D4
hypercenterC5×#555D3
hypocenterC3C5×#3303
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C4×C5×D4 ◁ C5×#555

796 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 32 points:

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

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, 185788);