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C5×#81800 #14439210

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

Aliases

direct productC5×#81800

Splittings

FittingC3×C5×#494 ⋊ C2
HallC3×C5 ⋊ #3152
SylowC3 ⋊ C5×#3152

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#494C2
socleC22×C3×C5C22×D4
prime radicalC5×#5725C2
hypercenterC5×#494D3
hypocenterC3C5×#3152
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#494

1104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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

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, 164908);