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C3×D3185 #34062019

order19110
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D3185
unambiguous semidirect productC5⋊(C3×D637)

Splittings

Fitting, HallC3×C5×C13×C49 ⋊ C2
derived, HallC5×C13×C49 ⋊ C2×C3
HallC3×C13×C49 ⋊ D5
HallC3×C5×C49 ⋊ D13
HallC13×C49 ⋊ C3×D5
HallC5×C49 ⋊ C3×D13
HallC3×C5×C13 ⋊ D49
HallC3×C49 ⋊ D65
HallC5×C13 ⋊ C3×D49
SylowC49 ⋊ C3×D65
HallC3×C13 ⋊ D245
HallC3×C5 ⋊ D637
SylowC13 ⋊ C3×D245
SylowC5 ⋊ C3×D637

Subgroups

subgroupG/H
center, hypercenterC3D3185
commutator, cosocle, hypocenterC5×C13×C49C2×C3
FrattiniC7C3×D455
FittingC3×C5×C13×C49C2
socleC3×C5×C7×C13D7
LCSG ▷ C5×C13×C49
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 70
transitive degreeμt(G) = 9555

A minimal faithful permutation representation — 2 generators on 70 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);(5,8)(6,7)(10,57)(11,56)(12,55)(13,54)(14,53)(15,52)(16,51)(17,50)(18,49)(19,48)(20,47)(21,46)(22,45)(23,44)(24,43)(25,42)(26,41)(27,40)(28,39)(29,38)(30,37)(31,36)(32,35)(33,34)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)

Conjugacy classes & character table

4782 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D13×D245, C3×D49×D65, C3×D5×D637, …
maximal normal subgroup ofC3×D13×D245, C3×D49×D65, C3×D5×D637, …
maximal quotient ofC3×Dic3185, C2×C3×D3185

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 12);