Finite Group Databasebeta

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C5×#82160 #14326683

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C23×C4

Aliases

direct productC5×#82160

Splittings

HallC3×C5 ⋊ #2345
SylowC3 ⋊ C5×#2345

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC22×C3×C5×C4⋊C4C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
cosocleC23×C3C24×C5
hypercenterC22×C5×C4⋊C4D3
hypocenterC3C5×#2345
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C22×C5×C4⋊C4

1096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 4 generators on 28 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 52381);