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C5×#70124 #14303073

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#70124

Splittings

FittingC2×C3×C5×#101 ⋊ C2
HallC3×C5 ⋊ #1915
SylowC3 ⋊ C5×#1915

Subgroups

subgroupG/H
centerC2×C5#4956
commutatorC23×C3C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C5×#101C2
socleC2×C3×C5#386
prime radicalC2×C5×#235C22
cosocleC22×C3×C4C23×C5
hypercenterC2×C5×#101D3
hypocenterC3C5×#1915
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C2×C5×#101

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 40 points:

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

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 28771);