Finite Group Databasebeta

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C5×#69444 #14283110

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

Aliases

direct productC5×#69444

Splittings

FittingC3×C4×C5×C22⋊C4 ⋊ C2
HallC3×C5 ⋊ #1507
SylowC3 ⋊ C5×#1507

Subgroups

subgroupG/H
centerC22×C5C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C4×C5×C22⋊C4C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C5×#930C2
cosocleC22×C3×C4C23×C5
hypercenterC4×C5×C22⋊C4D3
hypocenterC3C5×#1507
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ C4×C5×C22⋊C4

692 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 24 points:

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

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, 8808);