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C5×#68743 #14303595

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

Aliases

direct productC5×#68743

Splittings

HallC3×C5 ⋊ #1922
SylowC3 ⋊ C5×#1922

Subgroups

subgroupG/H
centerC2×C4×C5D3×D4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#339C2
socleC22×C3×C5C4×D4
prime radicalC23×C3×C5#41
cosocleC22×C3×C4C23×C5
hypercenterC5×#339D3
hypocenterC3C5×#1922
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C5×#339

372 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)(6,7,8)(9,11,12,15)(10,14,13,16)(17,20)(18,22)(19,26)(21,24)(23,28)(25,29)(27,30)(31,32);(7,8)(10,13)(14,16)(17,19,21,27,22,28,29,32)(18,23,25,31,20,26,24,30);(9,10)(11,14)(12,13)(15,16)(17,18,21,25,22,20,29,24)(19,23,27,31,28,26,32,30)

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, 29293);