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C3×D5225 #44535438

order31350
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D5225
unambiguous semidirect productC11⋊(C3×D475)
unambiguous semidirect productC25⋊(C3×D209)

Splittings

Fitting, HallC3×C11×C19×C25 ⋊ C2
derived, HallC11×C19×C25 ⋊ C2×C3
HallC3×C19×C25 ⋊ D11
HallC3×C11×C25 ⋊ D19
HallC3×C11×C19 ⋊ D25
HallC19×C25 ⋊ C3×D11
HallC11×C25 ⋊ C3×D19
HallC11×C19 ⋊ C3×D25
HallC3×C25 ⋊ D209
HallC3×C19 ⋊ D275
HallC3×C11 ⋊ D475
SylowC25 ⋊ C3×D209
SylowC19 ⋊ C3×D275
SylowC11 ⋊ C3×D475

Subgroups

subgroupG/H
center, hypercenterC3D5225
commutator, cosocle, hypocenterC11×C19×C25C2×C3
FrattiniC5C3×D1045
FittingC3×C11×C19×C25C2
socleC3×C5×C11×C19D5
LCSG ▷ C11×C19×C25
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 58
transitive degreeμt(G) = 15675

A minimal faithful permutation representation — 2 generators on 58 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);(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(30,39)(31,38)(32,37)(33,36)(34,35)(41,58)(42,57)(43,56)(44,55)(45,54)(46,53)(47,52)(48,51)(49,50)

Conjugacy classes & character table

7842 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 11);