Finite Group Databasebeta

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C5×#83696 #14471982

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

Aliases

direct productC5×#83696

Splittings

HallC3×C5 ⋊ #3363
SylowC3 ⋊ C5×#3363

Subgroups

subgroupG/H
centerC22×C5C22×#67
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#557C2
socle, prime radicalC22×C3×C5C22×D4
hypercenterC5×#557D3
hypocenterC3C5×#3363
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C4×C5×Q8 ◁ C5×#557

672 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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

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, 197680);