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C5×D19×D69 #39910768

order26220
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D19×D69
unambiguous semidirect product(C3×D19)⋊(C5×D23)
unambiguous semidirect product(C23×D19)⋊(C5×D3)

Splittings

Fitting, socle, HallC3×C5×C19×C23 ⋊ C22
derived, HallC3×C19×C23 ⋊ C22×C5
HallC5×C19×C23 ⋊ C2×D3
HallC19×C23 ⋊ C2×C5×D3
HallC3×C5×C23 ⋊ C2×D19
HallC3×C5×C19 ⋊ C2×D23
HallC5×C23 ⋊ D3×D19
HallC5×C19 ⋊ C2×D69
HallC3×C23 ⋊ C2×C5×D19
HallC3×C19 ⋊ C2×C5×D23
SylowC23 ⋊ C5×D3×D19
SylowC19 ⋊ C2×C5×D69
HallC3×C5 ⋊ D19×D23
SylowC3 ⋊ C5×D19×D23

Subgroups

subgroupG/H
center, hypercenterC5D19×D69
commutator, cosocle, hypocenterC3×C19×C23C22×C5
FrattiniC1G
Fitting, socleC3×C5×C19×C23C22
LCSG ▷ C3×C19×C23
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 6555

A minimal faithful permutation representation — 2 generators on 50 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(25,26)(27,28,30,32,34,36,38,40,42,44,45,43,41,39,37,35,33,31,29)(46,47,48,49,50);(1,2,4,6,8,10,12,14,16,18,20,22,23,21,19,17,15,13,11,9,7,5,3)(24,25,26)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)

Conjugacy classes & character table

1980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 58);