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C3×D6061 #49138306

order36366
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D6061
unambiguous semidirect productC11⋊(C3×D551)
unambiguous semidirect productC29⋊(C3×D209)

Splittings

Fitting, socle, HallC3×C11×C19×C29 ⋊ C2
derived, HallC11×C19×C29 ⋊ C2×C3
HallC3×C19×C29 ⋊ D11
HallC3×C11×C29 ⋊ D19
HallC3×C11×C19 ⋊ D29
HallC19×C29 ⋊ C3×D11
HallC11×C29 ⋊ C3×D19
HallC11×C19 ⋊ C3×D29
HallC3×C29 ⋊ D209
HallC3×C19 ⋊ D319
HallC3×C11 ⋊ D551
SylowC29 ⋊ C3×D209
SylowC19 ⋊ C3×D319
SylowC11 ⋊ C3×D551

Subgroups

subgroupG/H
center, hypercenterC3D6061
commutator, cosocle, hypocenterC11×C19×C29C2×C3
FrattiniC1G
Fitting, socleC3×C11×C19×C29C2
LCSG ▷ C11×C19×C29
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 62
transitive degreeμt(G) = 18183

A minimal faithful permutation representation — 2 generators on 62 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)(34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62);(5,14)(6,13)(7,12)(8,11)(9,10)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(35,62)(36,61)(37,60)(38,59)(39,58)(40,57)(41,56)(42,55)(43,54)(44,53)(45,52)(46,51)(47,50)(48,49)

Conjugacy classes & character table

9096 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36366, 9);