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C5×#69470 #14283196

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

Aliases

direct productC5×#69470

Splittings

FittingC3×C4×C5×C4⋊C4 ⋊ C2
HallC3×C5 ⋊ #1509
SylowC3 ⋊ C5×#1509

Subgroups

subgroupG/H
centerC22×C5C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C4×C5×C4⋊C4C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#930C22
cosocleC22×C3×C4C23×C5
hypercenterC4×C5×C4⋊C4D3
hypocenterC3C5×#1509
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ C4×C5×C4⋊C4

484 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)(10,14)(13,16)(17,19,21,20)(18,22,23,24);(7,8)(9,10)(11,16)(12,14)(13,15)(17,18)(19,22)(20,24)(21,23);(10,13)(11,15)(14,16)(18,22,23,24)

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, 8894);