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C5×#70136 #14301702

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

Aliases

direct productC5×#70136

Splittings

FittingC3×C5×#413 ⋊ C2
HallC3×C5 ⋊ #1891
SylowC3 ⋊ C5×#1891

Subgroups

subgroupG/H
centerC4×C5#882
commutatorC23×C3C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#413C2
socleC2×C3×C5#386
prime radicalC5×#5828C2
cosocleC22×C3×C4C23×C5
hypercenterC5×#413D3
hypocenterC3C5×#1891
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C22×C4×C5 ◁ C5×#413

684 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3,4,5)(6,7,8)(9,11)(10,14)(12,20)(13,18)(15,17)(16,24)(19,21)(22,23);(7,8)(9,10,12,16,13,15,21,23)(11,14,20,24,18,17,19,22);(9,10,12,16,13,15,21,23)(11,17,19,24,18,14,20,22)

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, 27400);