Finite Group Databasebeta

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C5×#68564 #14287409

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#68564

Splittings

HallC3×C5 ⋊ #1591
SylowC3 ⋊ C5×#1591

Subgroups

subgroupG/H
centerC2×C4×C5D3×D4
commutatorC2×C3×C4C22×C4×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#335C2
socle, prime radicalC22×C3×C5C4×D4
cosocleC3×C42C23×C5
hypercenterC5×#335D3
hypocenterC3C5×#1591
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C42×C5 ◁ C5×#335

304 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 1920

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 13107);