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C5×D2691 #41002086

order26910
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D2691
unambiguous semidirect productC9⋊(C5×D299)
unambiguous semidirect productC13⋊(C5×D207)
unambiguous semidirect productC23⋊(C5×D117)

Splittings

Fitting, HallC5×C9×C13×C23 ⋊ C2
derived, HallC9×C13×C23 ⋊ C2×C5
HallC5×C13×C23 ⋊ D9
HallC5×C9×C23 ⋊ D13
HallC5×C9×C13 ⋊ D23
HallC13×C23 ⋊ C5×D9
HallC9×C23 ⋊ C5×D13
HallC9×C13 ⋊ C5×D23
HallC5×C23 ⋊ D117
HallC5×C13 ⋊ D207
HallC5×C9 ⋊ D299
SylowC23 ⋊ C5×D117
SylowC13 ⋊ C5×D207
SylowC9 ⋊ C5×D299

Subgroups

subgroupG/H
center, hypercenterC5D2691
commutator, cosocle, hypocenterC9×C13×C23C2×C5
FrattiniC3C5×D897
FittingC5×C9×C13×C23C2
socleC3×C5×C13×C23D3
LCSG ▷ C9×C13×C23
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 13455

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

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

Conjugacy classes & character table

6735 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 13);