Finite Group Databasebeta

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C5×#68073 #14280609

order1920
automorphism?
homologyAbelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C8

Aliases

direct productC5×#68073

Splittings

FittingC3×C5×#322 ⋊ C2
HallC3×C5 ⋊ #1453
SylowC3 ⋊ C5×#1453

Subgroups

subgroupG/H
centerC42×C5C22×D3
commutatorC22×C3C2×C42×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#322C2
socleC22×C3×C5C2×C42
prime radicalC22×C5×D3C42
cosocleC3×C42C23×C5
hypercenterC5×#322D3
hypocenterC3C5×#1453
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C42×C5 ◁ C5×#322

380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 960

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 6307);