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C5×#68459 #14289757

order1920
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#68459

Splittings

FittingC3×C5×#332 ⋊ C2
HallC3×C5 ⋊ #1637
SylowC3 ⋊ C5×#1637

Subgroups

subgroupG/H
centerC22×C5#882
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#332C2
socleC22×C3×C5#120
prime radicalC2×C5×D12D4
hypercenterC5×#332D3
hypocenterC3C5×#1637
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#332

456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 15455);