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C2×C5×D1287 #38787927

order25740
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D1287
unambiguous semidirect product(C2×C9)⋊(C5×D143)
unambiguous semidirect product(C2×C13)⋊(C5×D99)

Splittings

FittingC2×C5×C9×C11×C13 ⋊ C2
derived, HallC9×C11×C13 ⋊ C22×C5
HallC5×C9×C11×C13 ⋊ C22
HallC5×C11×C13 ⋊ C2×D9
HallC5×C9×C13 ⋊ C2×D11
HallC5×C9×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C5×D9
HallC9×C13 ⋊ C2×C5×D11
HallC9×C11 ⋊ C2×C5×D13
HallC5×C13 ⋊ C2×D99
HallC5×C11 ⋊ C2×D117
HallC5×C9 ⋊ C2×D143
SylowC13 ⋊ C2×C5×D99
SylowC11 ⋊ C2×C5×D117
SylowC9 ⋊ C2×C5×D143

Subgroups

subgroupG/H
center, hypercenterC2×C5D1287
commutator, cosocle, hypocenterC9×C11×C13C22×C5
FrattiniC3C2×C5×D429
FittingC2×C5×C9×C11×C13C2
socleC2×C3×C5×C11×C13D3
LCSG ▷ C9×C11×C13
UCSC1 ◁ C2×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 12870

A minimal faithful permutation representation — 2 generators on 40 points:

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

Conjugacy classes & character table

6450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 158);