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C5×#79594 #14435571

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

Aliases

direct productC5×#79594

Splittings

FittingC3×C4×C5×D8 ⋊ C2
HallC3×C5 ⋊ #3118
SylowC3 ⋊ C5×#3118

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C4×C5×D8C2
socleC22×C3×C5C22×D4
prime radicalC5×#5156C2
hypercenterC4×C5×D8D3
hypocenterC3C5×#3118
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C4×C5×D8

812 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 4 generators on 32 points:

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

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, 161269);