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C5×#70786 #14280924

order1920
automorphism?
homologyAbelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC5×#70786

Splittings

HallC3×C5 ⋊ #1461
SylowC3 ⋊ C5×#1461

Subgroups

subgroupG/H
centerC2×C4×C5(C2×D3)⋊C4
commutatorC22×C3C22×C5×C8
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#431C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22×C4
cosocleC22×C3×C4C23×C5
hypercenterC5×#431D3
hypocenterC3C5×#1461
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C2×C42×C5 ◁ C5×#431

496 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)(6,7,8)(9,11,13,12)(10,14,16,15)(17,20,21,28)(18,23,24,30)(19,26,27,32)(22,29,25,31);(7,8)(17,19,21,27)(18,22,24,25)(20,26,28,32)(23,29,30,31);(9,10,12,15,13,16,11,14)(17,18)(19,25,27,22)(20,23)(21,24)(26,31,32,29)(28,30)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 6622);