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C5×#78640 #14424114

order1920
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C26

Aliases

direct productC5×#78640

Splittings

FittingC3×C5×#407 ⋊ C2
HallC3×C5 ⋊ #3007
SylowC3 ⋊ C5×#3007

Subgroups

subgroupG/H
centerC22×C5C22×D12
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#407C2
socleC22×C3×C5C22×D4
prime radicalC22×C5×#235C2
hypercenterC5×#407D3
hypocenterC3C5×#3007
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ C5×#407

1508 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 4 generators on 28 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 149812);