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C5×#68147 #14281362

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#68147

Splittings

FittingC3×C5×#324 ⋊ C2
HallC3×C5 ⋊ #1472
SylowC3 ⋊ C5×#1472

Subgroups

subgroupG/H
centerC22×C5D3×C22⋊C4
commutatorC23×C3C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#324C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C5×D3C2×C4
cosocleC22×C3×C4C23×C5
hypercenterC5×#324D3
hypocenterC3C5×#1472
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#324

540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 480

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 7060);