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C5×D3393 #46800227

order33930
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D3393
unambiguous semidirect productC9⋊(C5×D377)
unambiguous semidirect productC13⋊(C5×D261)
unambiguous semidirect productC29⋊(C5×D117)

Splittings

Fitting, HallC5×C9×C13×C29 ⋊ C2
derived, HallC9×C13×C29 ⋊ C2×C5
HallC5×C13×C29 ⋊ D9
HallC5×C9×C29 ⋊ D13
HallC5×C9×C13 ⋊ D29
HallC13×C29 ⋊ C5×D9
HallC9×C29 ⋊ C5×D13
HallC5×C29 ⋊ D117
HallC9×C13 ⋊ C5×D29
HallC5×C13 ⋊ D261
HallC5×C9 ⋊ D377
SylowC29 ⋊ C5×D117
SylowC13 ⋊ C5×D261
SylowC9 ⋊ C5×D377

Subgroups

subgroupG/H
center, hypercenterC5D3393
commutator, cosocle, hypocenterC9×C13×C29C2×C5
FrattiniC3C5×D1131
FittingC5×C9×C13×C29C2
socleC3×C5×C13×C29D3
LCSG ▷ C9×C13×C29
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 56
transitive degreeμt(G) = 16965

A minimal faithful permutation representation — 2 generators on 56 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)(28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56);(7,14)(8,13)(9,12)(10,11)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(29,56)(30,55)(31,54)(32,53)(33,52)(34,51)(35,50)(36,49)(37,48)(38,47)(39,46)(40,45)(41,44)(42,43)

Conjugacy classes & character table

8490 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33930, 13);