Finite Group Databasebeta

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C5×#68946 #14300778

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#68946

Splittings

FittingC3×C5×#341 ⋊ C2
HallC3×C5 ⋊ #1876
SylowC3 ⋊ C5×#1876

Subgroups

subgroupG/H
centerC2×C4×C5D3×D4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#341C2
socleC22×C3×C5C4×D4
prime radicalC2×C5×#904C2
cosocleC22×C3×C4C23×C5
hypercenterC5×#341D3
hypocenterC3C5×#1876
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C5×#341

648 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 28 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 26476);