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C3×D3245 #34085688

order19470
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D3245
unambiguous semidirect productC5⋊(C3×D649)
unambiguous semidirect productC11⋊(C3×D295)
unambiguous semidirect productC59⋊(C3×D55)

Splittings

Fitting, socle, HallC3×C5×C11×C59 ⋊ C2
derived, HallC5×C11×C59 ⋊ C2×C3
HallC3×C11×C59 ⋊ D5
HallC3×C5×C59 ⋊ D11
HallC11×C59 ⋊ C3×D5
HallC5×C59 ⋊ C3×D11
HallC3×C59 ⋊ D55
HallC3×C5×C11 ⋊ D59
SylowC59 ⋊ C3×D55
HallC5×C11 ⋊ C3×D59
HallC3×C11 ⋊ D295
HallC3×C5 ⋊ D649
SylowC11 ⋊ C3×D295
SylowC5 ⋊ C3×D649

Subgroups

subgroupG/H
center, hypercenterC3D3245
commutator, cosocle, hypocenterC5×C11×C59C2×C3
FrattiniC1G
Fitting, socleC3×C5×C11×C59C2
LCSG ▷ C5×C11×C59
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 78
transitive degreeμt(G) = 9735

A minimal faithful permutation representation — 2 generators on 78 points:

(1,2,3)(4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78);(5,8)(6,7)(10,19)(11,18)(12,17)(13,16)(14,15)(21,78)(22,77)(23,76)(24,75)(25,74)(26,73)(27,72)(28,71)(29,70)(30,69)(31,68)(32,67)(33,66)(34,65)(35,64)(36,63)(37,62)(38,61)(39,60)(40,59)(41,58)(42,57)(43,56)(44,55)(45,54)(46,53)(47,52)(48,51)(49,50)

Conjugacy classes & character table

4872 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19470, 9);