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C5×#69104 #14315121

order1920
automorphism?
homologyAbelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C22

Aliases

direct productC5×#69104

Splittings

FittingC3×C5×C22⋊C16 ⋊ C2
HallC3×C5 ⋊ #2169
SylowC3 ⋊ C5×#2169

Subgroups

subgroupG/H
centerC2×C5×C8C22×D3
commutatorC22×C3C22×C5×C8
FrattiniC2×C8C22×C5×D3
FittingC3×C5×C22⋊C16C2
socleC22×C3×C5C22×C8
prime radicalC2×C5×#67C8
cosocleC2×C3×C8C23×C5
hypercenterC5×C22⋊C16D3
hypocenterC3C5×#2169
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C5×C8 ◁ C5×C22⋊C16

324 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)(7,8)(13,15,17,24,18,19,22,27,16,23,25,28,26,14,20,21);(6,7,8)(10,12)(14,19)(15,23)(21,27)(24,28);(9,10)(11,12)(13,14,17,21,18,15,22,24,16,19,25,27,26,23,20,28)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 40819);