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C5×#72082 #14316103

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

Aliases

direct productC5×#72082

Splittings

FittingC2×C3×C5×#135 ⋊ C2
HallC3×C5 ⋊ #2186
SylowC3 ⋊ C5×#2186

Subgroups

subgroupG/H
centerC22×C5C2×#213
commutator, cosocleC2×C3×C8C23×C5
FrattiniC2×C8C22×C5×D3
FittingC2×C3×C5×#135C2
socleC22×C3×C5C2×D8
hypercenterC2×C5×#135D3
hypocenterC3C5×#2186
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C22×C5×C8 ◁ C2×C5×#135

460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 3 generators on 28 points:

(1,2,3,4,5)(6,7,8)(10,12)(13,15,17,18)(14,20,21,26)(16,22,25,23)(19,24,27,28);(13,14)(15,20)(16,24)(17,21)(18,26)(19,23)(22,27)(25,28);(7,8)(9,10)(11,12)(14,19)(15,18)(16,23)(20,28)(21,27)(22,25)(24,26)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 41801);