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C5×#71432 #14312860

order1920
automorphism?
homologyAbelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C23

Aliases

direct productC5×#71432

Splittings

FittingC2×C3×C5×M32 ⋊ C2
HallC3×C5 ⋊ #2113
SylowC3 ⋊ C5×#2113

Subgroups

subgroupG/H
centerC2×C5×C8C22×D3
commutatorC22×C3C22×C5×C8
FrattiniC2×C8C22×C5×D3
FittingC2×C3×C5×M32C2
socleC22×C3×C5C22×C8
prime radicalC2×C5×#235C4
cosocleC2×C3×C8C23×C5
hypercenterC2×C5×M32D3
hypocenterC3C5×#2113
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C5×C8 ◁ C2×C5×M32

456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 3 generators on 44 points:

(1,2,3,4,5)(6,7,8)(15,23)(19,29)(24,35)(25,36)(30,39)(31,40)(37,43)(41,44);(7,8)(10,12)(13,15)(14,19)(16,24)(17,25)(18,23)(20,30)(21,31)(22,29)(26,37)(27,35)(28,36)(32,41)(33,39)(34,40)(38,43)(42,44);(7,8)(9,10)(11,12)(13,14,16,20,17,21,26,32,18,22,27,33,28,34,38,42)(15,19,24,30,25,31,37,41,23,29,35,39,36,40,43,44)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 38558);