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C5×#68177 #14282448

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

Aliases

direct productC5×#68177

Splittings

FittingC3×C5×D4⋊C8 ⋊ C2
HallC3×C5 ⋊ #1494
SylowC3 ⋊ C5×#1494

Subgroups

subgroupG/H
centerC2×C4×C5D3×D4
commutatorC2×C3×C4C22×C4×C5
FrattiniC42C22×C5×D3
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#938C4
cosocleC3×C42C23×C5
hypercenterC5×D4⋊C8D3
hypocenterC3C5×#1494
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C42×C5 ◁ C5×D4⋊C8

460 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)(7,8)(9,12,14,13)(10,15,11,16)(18,23)(19,25)(24,30)(26,31);(6,7,8)(9,11)(10,14)(12,15)(13,16)(17,19)(18,22)(20,26)(21,25)(23,29)(24,28)(27,31)(30,32);(9,10,13,15,14,11,12,16)(17,18,20,24,21,23,27,30)(19,22,26,28,25,29,31,32)

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, 8146);