Finite Group Databasebeta

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C5×#78822 #14430213

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

Aliases

direct productC5×#78822

Splittings

HallC3×C5 ⋊ #3076
SylowC3 ⋊ C5×#3076

Subgroups

subgroupG/H
centerC2×C4×C5D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#416C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×C5×#41C22
hypercenterC5×#416D3
hypocenterC3C5×#3076
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C5×#416

776 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)(17,20,22,21)(18,24,25,29)(19,27,28,30)(23,31,32,26);(17,19)(18,23)(20,27)(21,30)(22,28)(24,31)(25,32)(26,29);(7,8)(9,11,12,16)(10,13,14,15);(9,10,12,14)(11,15,16,13)(17,18)(19,26)(20,24)(21,29)(22,25)(23,27)(28,31)(30,32)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 155911);