Finite Group Databasebeta

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C5×#74158 #14327768

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

Aliases

direct productC5×#74158

Splittings

HallC3×C5 ⋊ #2355
SylowC3 ⋊ C5×#2355

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC3×C5×#382C2
socle, prime radicalC23×C3×C5C24
cosocleC23×C3C24×C5
hypercenterC5×#382D3
hypocenterC3C5×#2355
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C5×#382

960 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 1920

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 53466);